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Technical Design ReportIssue: 1Revision: 0Reference: ATLAS TDR 4, CERN/LHCC 97-16Created: 30 April 1997Last modified: 30 April 1997Prepared By: ATLAS Inner Detector Community

Volume I

ATLAS Inner Detector Volume ITechnical Design Report 30 April 1997

ii

All trademarks, copyright names and products referred to in this document are acknowledged as such.


ATLAS Collaboration iii

ATLAS Collaboration

ArmeniaYerevan Physics Institute, Yerevan

AustraliaResearch Centre for High Energy Physics, Melbourne University, MelbourneAustralian Nuclear Science and Technology Organisation, SydneyUniversity of Sydney, Sydney

AustriaInstitut für Experimentalphysik der Leopold-Franzens-Universität Innsbruck, Innsbruck

Azerbaijan RepublicInstitute of Physics, Azerbaijan Academy of Science, Baku

Republic of BelarusInstitute of Physics of the Academy of Science of Belarus, Minsk

BrazilUniversidade Federal do Rio de Janeiro, COPPE/EE/IF, Rio de JaneiroInstituto de Fisica, Universidade de Sao Paulo, Sao Paulo

CanadaUniversity of Alberta, EdmontonDepartment of Physics, University of British Columbia, VancouverUniversity of Carleton/C.R.P.P., CarletonGroup of Particle Physics, University of Montreal, MontrealDepartment of Physics, University of Toronto, TorontoTRIUMF, VancouverUniversity of Victoria, Victoria

CERNEuropean Laboratory for Particle Physics (CERN), Geneva

Czech RepublicAcademy of Sciences of the Czech Republic, Institute of Physics, PragueCharles University, Faculty of Mathematics and Physics, PragueCzech Technical University in Prague, Faculty of Nuclear Sciences andPhysical Engineering, Faculty of Mechanical Engineering, Prague

DenmarkNiels Bohr Institute, University of Copenhagen, Copenhagen

FinlandHelsinki Institute of Physics, Helsinki

FranceLaboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), IN2P3-CNRS, Annecy-le-VieuxUniversité Blaise Pascal, IN2P3-CNRS, Clermont-FerrandInstitut des Sciences Nucléaires de Grenoble, IN2P3-CNRS-Université Joseph Fourier, GrenobleCentre de Physique des Particules de Marseille, IN2P3-CNRS, MarseilleLaboratoire de l’Accélérateur Linéaire, IN2P3-CNRS, OrsayLPNHE, Universités de Paris VI et VII, IN2P3-CNRS, ParisCEA, DSM/DAPNIA, Centre d’Etudes de Saclay, Gif-sur-Yvette


iv ATLAS Collaboration

Republic of GeorgiaInstitute of Physics of the Georgian Academy of Sciences, TbilisiTbilisi State University, Tbilisi

GermanyPhysikalisches Institut, Universität Bonn, BonnInstitut für Physik, Universität Dortmund, DortmundFakultät für Physik, Albert-Ludwigs-Universität, FreiburgInstitut für Hochenergiephysik der Universität Heidelberg, HeidelbergInstitut für Informatik, Friedrich-Schiller-Universität Jena, JenaInstitut für Physik, Johannes-Gutenberg Universität Mainz, MainzLehrstuhl für Informatik V, Universität Mannheim, MannheimSektion Physik, Ludwig-Maximilian-Universität München, MünchenMax-Planck-Institut für Physik, MünchenFachbereich Physik, Universität Siegen, SiegenFachbereich Physik, Bergische Universität, Wuppertal

GreeceAthens National Technical University, AthensAthens University, AthensAristotle University of Thessaloniki, Thessaloniki

IsraelDepartment of Physics, Technion, HaifaRaymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel-AvivUniversity, Tel-AvivDepartment of Particle Physics, The Weizmann Institute of Science, Rehovot

ItalyDipartimento di Fisica dell’ Università della Calabria e I.N.F.N., CosenzaLaboratori Nazionali di Frascati dell’ I.N.F.N., FrascatiDipartimento di Fisica dell’ Università di Genova e I.N.F.N., GenovaDipartimento di Fisica dell’ Università di Lecce e I.N.F.N., LecceDipartimento di Fisica dell’ Università di Milano e I.N.F.N., MilanoDipartimento di Scienze Fisiche, Università di Napoli ‘Federico II’ e I.N.F.N., NapoliDipartimento di Fisica Nucleare e Teorica dell’ Università di Pavia e I.N.F.N., PaviaDipartimento di Fisica dell’ Università di Pisa e I.N.F.N., PisaDipartimento di Fisica dell’ Università di Roma ‘La Sapienza’ e I.N.F.N., RomaDipartimento di Fisica dell’ Università di Roma ‘Tor Vergata’ e I.N.F.N., RomaDipartimento di Fisica dell’ Università di Roma ‘Roma Tre’ e I.N.F.N., RomaDipartimento di Fisica dell’ Università di Udine, Gruppo collegato di Udine I.N.F.N. Trieste, Udine

JapanDepartment of Information Science, Fukui University, FukuiHiroshima Institute of Technology, HiroshimaDepartment of Physics, Hiroshima University, Higashi-HiroshimaKEK, National Laboratory for High Energy Physics, TsukubaDepartment of Physics, Faculty of Science, Kobe University, KobeKyoto University of Education, Kyoto-shiNaruto University of Education, Naruto-shiDepartment of Physics, Faculty of Science, Shinshu University, MatsumotoInternational Center for Elementary Particle Physics, University of Tokyo, TokyoPhysics Department, Tokyo Metropolitan University, TokyoTokyo University of Agriculture and Technology, Department of Applied Physics, Tokyo

KazakhstanHigh-Energy Physics Institute of the Kazakh Academy of Sciences, Almaty


ATLAS Collaboration v

MoroccoFaculté des Sciences Aïn Chock, Université Hassan II, Casablanca, and Université Mohamed V, Rabat

NetherlandsFOM - Institute SAF NIKHEF and University of Amsterdam/NIKHEF, AmsterdamUniversity of Nijmegen/NIKHEF, Nijmegen

NorwayUniversity of Bergen, BergenUniversity of Oslo, Oslo

PolandHenryk Niewodniczanski Institute of Nuclear Physics, CracowFaculty of Physics and Nuclear Techniques of the Academy of Mining and Metallurgy, Cracow

PortugalLaboratorio de Instrumentação e Física Experimental de Partículas (University of Lisboa, University ofCoimbra, University Católica-Figueira da Foz and University Nova de Lisboa), Lisbon

RomaniaInstitute of Atomic Physics, Bucharest

RussiaInstitute for Theoretical and Experimental Physics (ITEP), MoscowP.N. Lebedev Institute of Physics, MoscowMoscow Engineering and Physics Institute (MEPhI), MoscowMoscow State University, Institute of Nuclear Physics, MoscowBudker Institute of Nuclear Physics (BINP), NovosibirskInstitute for High Energy Physics (IHEP), ProtvinoPetersburg Nuclear Physics Institute (PNPI), Gatchina, St. Petersburg

JINRJoint Institute for Nuclear Research, Dubna

Slovak RepublicBratislava University, Bratislava, and Institute of Experimental Physics of the Slovak Academy ofSciences, Kosice

SloveniaJozef Stefan Institute and Department of Physics, University of Ljubljana, Ljubljana

SpainInstitut de Física d’Altes Energies (IFAE), Universidad Autónoma de Barcelona, Bellaterra, BarcelonaPhysics Department, Universidad Autónoma de Madrid, MadridInstituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia - CSIC, Burjassot, Valencia

SwedenFysika institutionen, Lunds universitet, LundRoyal Institute of Technology (KTH), StockholmUniversity of Stockholm, StockholmUppsala University, Department of Radiation Sciences, Uppsala

SwitzerlandLaboratory for High Energy Physics, University of Bern, BernSection de Physique, Université de Genève, Geneva

TurkeyDepartment of Physics, Bogaziçi University, Istanbul


vi ATLAS Collaboration

United KingdomSchool of Physics and Space Research, The University of Birmingham, BirminghamCavendish Laboratory, Cambridge University, CambridgeDepartment of Physics and Astronomy, University of Edinburgh, EdinburghDepartment of Physics and Astronomy, University of Glasgow, GlasgowSchool of Physics and Chemistry, Lancaster University, LancasterDepartment of Physics, Oliver Lodge Laboratory, University of Liverpool, LiverpoolDepartment of Physics, Queen Mary and Westfield College, University of London, LondonDepartment of Physics, Royal Holloway and Bedford New College, University of London, EghamDepartment of Physics and Astronomy, University College London, LondonDepartment of Physics and Astronomy, University of Manchester, ManchesterDepartment of Physics, Oxford University, OxfordRutherford Appleton Laboratory, Chilton, DidcotDepartment of Physics, University of Sheffield, Sheffield

United States of AmericaState University of New York at Albany, New YorkArgonne National Laboratory, Argonne, IllinoisUniversity of Arizona, Tucson, ArizonaDepartment of Physics, The University of Texas at Arlington, Arlington, TexasLawrence Berkeley Laboratory and University of California, Berkeley, CaliforniaDepartment of Physics, Boston University, Boston, MassachusettsBrandeis University, Department of Physics, Waltham, MassachusettsBrookhaven National Laboratory (BNL), Upton, New YorkUniversity of Chicago, Enrico Fermi Institute, Chicago, IllinoisNevis Laboratory, Columbia University, Irvington, New YorkDepartment of Physics, Duke University, Durham, North CarolinaDepartment of Physics, Hampton University, VirginiaDepartment of Physics, Harvard University, Cambridge, MassachusettsIndiana University, Bloomington, IndianaUniversity of California, Irvine, CaliforniaMassachusetts Institute of Technology, Department of Physics, Cambridge, MassachusettsMichigan State University, Department of Physics and Astronomy, East Lansing, MichiganUniversity of New Mexico, New Mexico Center for Particle Physics, AlbuquerquePhysics Department, Norfolk State University, VirginiaPhysics Department, Northern Illinois University, DeKalb, IllinoisDepartment of Physics and Astronomy, University of OklahomaDepartment of Physics, University of Pennsylvania, Philadelphia, PennsylvaniaUniversity of Pittsburgh, Pittsburgh, PennsylvaniaDepartment of Physics and Astronomy, University of Rochester, Rochester, New YorkInstitute for Particle Physics, University of California, Santa Cruz, CaliforniaDepartment of Physics, Southern Methodist University, Dallas, TexasTufts University, Medford, MassachusettsHigh Energy Physics, University of Illinois, Urbana, IllinoisDepartment of Physics, Department of Mechanical Engineering, University of Washington, Seattle,WashingtonDepartment of Physics, University of Wisconsin, Madison, Wisconsin


ATLAS Collaboration vii


viii Acknowledgements

Acknowledgements

The Editors would like to thank Mario Ruggier for preparing the FrameMaker template uponwhich this document is based, and for his continuous help and competent advice. The Editorsalso warmly thank Michèle Jouhet and Marinette Glomet for processing the colour figures. Theadvice from Jean-Pierre Schnewlin and the rapid printing by the Print-shop staff are also greatlyappreciated. Finally, all participating Institutes would like to express their gratitude to theirsupport staff for the invaluable help in designing and prototyping the many parts of the InnerDetector.


Table Of Contents ix

Table Of Contents

ATLAS Collaboration . . . . . . . . . . . . . . . . . . . . iii

Acknowledgements . . . . . . . . . . . . . . . . . . . . . viii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 31.1 Purpose and Organisation of the Inner Detector TDR . . . . . . . 31.2 Overview of the ATLAS Inner Detector . . . . . . . . . . . . 4

1.2.1 Physics Goals . . . . . . . . . . . . . . . . . . . 41.2.2 The Inner Detector Layout . . . . . . . . . . . . . . 5

1.2.2.1 The Pixel Detector . . . . . . . . . . . . . . 71.2.2.2 The Semiconductor Tracker . . . . . . . . . . . 81.2.2.3 The Transition Radiation Tracker . . . . . . . . . 9

1.2.3 Summary of Performance . . . . . . . . . . . . . . 101.2.4 Material Budget . . . . . . . . . . . . . . . . . . 131.2.5 Evolution of the Layout since the Technical Proposal . . . . . 151.2.6 Radiation Environment . . . . . . . . . . . . . . . 15

1.3 Project Management, Schedule and Cost . . . . . . . . . . . . 171.3.1 Project Organisation . . . . . . . . . . . . . . . . 171.3.2 Overall Schedule and Milestones . . . . . . . . . . . . 181.3.3 Quality Assurance and Quality Control . . . . . . . . . . 191.3.4 Costs and Resources . . . . . . . . . . . . . . . . 20

1.4 References . . . . . . . . . . . . . . . . . . . . . . 21

2 Introduction to Performance . . . . . . . . . . . . . . . . . . 292.1 Overview . . . . . . . . . . . . . . . . . . . . . . . 292.2 Definitions and Nomenclature . . . . . . . . . . . . . . . 302.3 Performance Specifications. . . . . . . . . . . . . . . . . 30

2.3.1 Basic Specifications . . . . . . . . . . . . . . . . . 302.3.2 Pattern Recognition Specifications . . . . . . . . . . . 312.3.3 Physics Specifications . . . . . . . . . . . . . . . . 31

2.4 Simulation of Physics. . . . . . . . . . . . . . . . . . . 322.4.1 B-meson Decays . . . . . . . . . . . . . . . . . . 322.4.2 Single Particles . . . . . . . . . . . . . . . . . . 322.4.3 Hadronic Decays of Higgs Bosons. . . . . . . . . . . . 33

2.4.3.1 Properties of H → bb Events with mH = 400 GeV . . . 33

2.4.4 Minimum Bias Events . . . . . . . . . . . . . . . . 352.5 ATLAS Software . . . . . . . . . . . . . . . . . . . . 36

2.5.1 Overview of Different Software Steps . . . . . . . . . . 362.5.2 Code for Pattern Recognition and Track Fitting . . . . . . . 37

2.5.2.1 iPatRec . . . . . . . . . . . . . . . . . . 372.5.2.2 PixlRec . . . . . . . . . . . . . . . . . . 392.5.2.3 xKalman . . . . . . . . . . . . . . . . . 39

2.6 Pile-up at High Luminosity . . . . . . . . . . . . . . . . 402.7 References . . . . . . . . . . . . . . . . . . . . . . 41


x Table Of Contents

3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . 473.1 Layout. . . . . . . . . . . . . . . . . . . . . . . . 47

3.1.1 Pixel Detector . . . . . . . . . . . . . . . . . . 473.1.1.1 Pixel Barrel . . . . . . . . . . . . . . . . 473.1.1.2 Pixel End-caps . . . . . . . . . . . . . . . 493.1.1.3 Pixel Material . . . . . . . . . . . . . . . 50

3.1.2 SCT . . . . . . . . . . . . . . . . . . . . . . 513.1.2.1 SCT Barrel . . . . . . . . . . . . . . . . . 513.1.2.2 SCT End-caps . . . . . . . . . . . . . . . 523.1.2.3 SCT Material . . . . . . . . . . . . . . . . 55

3.1.3 TRT . . . . . . . . . . . . . . . . . . . . . . 573.1.3.1 TRT Barrel. . . . . . . . . . . . . . . . . 573.1.3.2 TRT End-caps . . . . . . . . . . . . . . . 593.1.3.3 TRT Straws . . . . . . . . . . . . . . . . 593.1.3.4 TRT Material . . . . . . . . . . . . . . . . 60

3.1.4 Services between Detectors . . . . . . . . . . . . . . 613.1.5 Differences between Engineering and Simulation Layouts . . . 62

3.1.5.1 Pixels . . . . . . . . . . . . . . . . . . 633.1.5.2 SCT . . . . . . . . . . . . . . . . . . . 633.1.5.3 TRT . . . . . . . . . . . . . . . . . . . 633.1.5.4 Services. . . . . . . . . . . . . . . . . . 63

3.2 Magnetic Field . . . . . . . . . . . . . . . . . . . . . 643.3 Rapidity Coverage . . . . . . . . . . . . . . . . . . . 653.4 Material . . . . . . . . . . . . . . . . . . . . . . . 67

3.4.1 Radiation Lengths . . . . . . . . . . . . . . . . . 683.4.1.1 Distributions . . . . . . . . . . . . . . . . 683.4.1.2 Consequences . . . . . . . . . . . . . . . 69

3.4.2 Absorption Lengths . . . . . . . . . . . . . . . . 713.4.2.1 Distributions . . . . . . . . . . . . . . . . 713.4.2.2 Consequences . . . . . . . . . . . . . . . 72

3.5 Pixels . . . . . . . . . . . . . . . . . . . . . . . . 743.5.1 Digitisation . . . . . . . . . . . . . . . . . . . 743.5.2 Simulation of Noise and Inefficiency. . . . . . . . . . . 753.5.3 Rapidity Coverage and Properties of Clusters . . . . . . . 763.5.4 Spatial Resolution . . . . . . . . . . . . . . . . . 773.5.5 Occupancy . . . . . . . . . . . . . . . . . . . 78

3.5.5.1 Occupancy per Column . . . . . . . . . . . . 793.5.5.2 Occupancy per Module . . . . . . . . . . . . 803.5.5.3 Cluster Width and Fraction of Merged Clusters . . . . 81

3.6 SCT. . . . . . . . . . . . . . . . . . . . . . . . . 833.6.1 Simulation of Signal and Digitisation . . . . . . . . . . 833.6.2 Cluster Widths . . . . . . . . . . . . . . . . . . 843.6.3 Spatial Resolution . . . . . . . . . . . . . . . . . 843.6.4 Comparison with Test-beam Results . . . . . . . . . . . 85


Table Of Contents xi

3.6.5 Occupancy . . . . . . . . . . . . . . . . . . . . 863.6.5.1 Occupancy per Module . . . . . . . . . . . . 873.6.5.2 Cluster Width and Fraction of Merged Clusters . . . . 88

3.7 TRT . . . . . . . . . . . . . . . . . . . . . . . . . 903.7.1 Introduction . . . . . . . . . . . . . . . . . . . 903.7.2 Time Response Model . . . . . . . . . . . . . . . . 903.7.3 Comparison with Test-beam Results . . . . . . . . . . . 91

3.7.3.1 dE/dx and Transition Radiation . . . . . . . . . 923.7.3.2 Drift-time Measurements. . . . . . . . . . . . 93

3.7.4 Simulation of Straw Response . . . . . . . . . . . . . 953.7.4.1 Simulation Conditions for Drift-time Measurement,

Rate and Occupancy Studies . . . . . . . . . . 953.7.4.2 Drift-time Measurement Efficiency . . . . . . . . 953.7.4.3 Spatial Resolution . . . . . . . . . . . . . . 96

3.7.5 Rates and Occupancies . . . . . . . . . . . . . . . 973.7.5.1 Total Charged Particle Rate . . . . . . . . . . . 983.7.5.2 Straw Hit Occupancy . . . . . . . . . . . . . 983.7.5.3 High-Threshold Hit Occupancy . . . . . . . . . 1013.7.5.4 Effect of Backsplash from Calorimeter . . . . . . . 102

3.8 References . . . . . . . . . . . . . . . . . . . . . . 102

4 Single Track Performance . . . . . . . . . . . . . . . . . . . 1034.1 Momentum Resolution . . . . . . . . . . . . . . . . . . 104

4.1.1 Basic Measurements . . . . . . . . . . . . . . . . 1044.1.2 Effect of Solenoidal Field . . . . . . . . . . . . . . . 1064.1.3 Sensitivity and Robustness . . . . . . . . . . . . . . 1064.1.4 Effect of Pile-up . . . . . . . . . . . . . . . . . . 107

4.2 Charge Determination . . . . . . . . . . . . . . . . . . 1084.3 Angular Resolution . . . . . . . . . . . . . . . . . . . 1104.4 Impact Parameter Resolution . . . . . . . . . . . . . . . . 111

4.4.1 Impact Parameter as a Function of pT and |η| . . . . . . . 112

4.5 Summary of Parameter Resolutions. . . . . . . . . . . . . . 1154.6 TR Performance . . . . . . . . . . . . . . . . . . . . 117

4.6.1 Effect of Pile-up . . . . . . . . . . . . . . . . . . 1204.7 References . . . . . . . . . . . . . . . . . . . . . . 120

5 Pattern Recognition . . . . . . . . . . . . . . . . . . . . . 1215.1 Isolated Tracks . . . . . . . . . . . . . . . . . . . . . 121

5.1.1 Efficiencies. . . . . . . . . . . . . . . . . . . . 1215.1.1.1 Definition of Efficiency . . . . . . . . . . . . 1215.1.1.2 Distributions . . . . . . . . . . . . . . . . 121

5.1.2 Tails of Distributions . . . . . . . . . . . . . . . . 1245.1.2.1 Muons . . . . . . . . . . . . . . . . . . 1245.1.2.2 Pions. . . . . . . . . . . . . . . . . . . 125


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5.1.3 Fake rate . . . . . . . . . . . . . . . . . . . . 1265.1.3.1 Definition of Fake Tracks . . . . . . . . . . . 1265.1.3.2 Distributions . . . . . . . . . . . . . . . . 126

5.1.4 Effect of Noise and Detector Inefficiency . . . . . . . . . 1285.1.5 Comparison with Specifications . . . . . . . . . . . . 129

5.2 Tracks in Jets . . . . . . . . . . . . . . . . . . . . . 1295.2.1 Track Quality. . . . . . . . . . . . . . . . . . . 1295.2.2 Selection Cuts for b-Tagging . . . . . . . . . . . . . 1345.2.3 Conclusions on Pattern Recognition in Jets . . . . . . . . 143

5.3 References . . . . . . . . . . . . . . . . . . . . . . 143

6 Physics Studies . . . . . . . . . . . . . . . . . . . . . . 1456.1 High-pT Electrons and QCD-Jet Rejection . . . . . . . . . . . 145

6.1.1 Datasets . . . . . . . . . . . . . . . . . . . . 1456.1.2 Event Selection and Analysis . . . . . . . . . . . . . 145

6.1.2.1 Calorimeter Selection . . . . . . . . . . . . . 1456.1.2.2 Track Reconstruction and Selection . . . . . . . . 148

6.1.3 Jet Rejection Rates . . . . . . . . . . . . . . . . . 1536.1.4 Further Jet Rejection . . . . . . . . . . . . . . . . 1556.1.5 Summary . . . . . . . . . . . . . . . . . . . . 156

6.2 Low-pT Electrons . . . . . . . . . . . . . . . . . . . . 157

6.2.1 J/ψ → e+e− . . . . . . . . . . . . . . . . . . . . . . . . .157

6.2.1.1 Kinematic Reconstruction of J/ψ . . . . . . . . . 1576.2.1.2 Rejection of Combinatorial Backgrounds using TR

Information . . . . . . . . . . . . . . . . 1596.2.2 Lepton b-Tagging . . . . . . . . . . . . . . . . . 160

6.2.2.1 Track Selection and Event Analysis . . . . . . . . 1606.2.2.2 Performance . . . . . . . . . . . . . . . . 161

6.3 Photon Identification. . . . . . . . . . . . . . . . . . . 1626.3.1 Background from Electrons . . . . . . . . . . . . . . 1636.3.2 Recovery of Converted Photons . . . . . . . . . . . . 165

6.3.2.1 Method for Conversion Identification . . . . . . . 1656.3.2.2 Performance . . . . . . . . . . . . . . . . 1666.3.2.3 π0 Rejection . . . . . . . . . . . . . . . . 168

6.4 Primary Vertex Reconstruction . . . . . . . . . . . . . . . 1706.5 V0 Reconstruction . . . . . . . . . . . . . . . . . . . . 172

6.5.1 Description of the V0 Finding Algorithm . . . . . . . . . 1726.5.2 Performance for Single V0 Events . . . . . . . . . . . . 173

6.6 Reconstruction of Exclusive B-decays . . . . . . . . . . . . . 1756.6.1 Reconstruction of Bd

0 → J/ψ Ks0 Events . . . . . . . . . . 175

6.6.2 Reconstruction of Bs0 → Ds

− π+ Events . . . . . . . . . . 177

6.7 Vertex b-Tagging . . . . . . . . . . . . . . . . . . . . 1796.7.1 Methods . . . . . . . . . . . . . . . . . . . . 1816.7.2 Track Selection . . . . . . . . . . . . . . . . . . 1816.7.3 Basic Performance . . . . . . . . . . . . . . . . . 182


Table Of Contents xiii

6.7.4 Possible Improvements . . . . . . . . . . . . . . . 1856.7.5 Degraded Performance . . . . . . . . . . . . . . . 1876.7.6 Results for mH = 100 GeV . . . . . . . . . . . . . . 188

6.7.7 Jet pT Dependence . . . . . . . . . . . . . . . . . 188

6.7.8 Impact on Physics . . . . . . . . . . . . . . . . . 1906.7.9 Conclusions on b-Tagging . . . . . . . . . . . . . . 193

6.8 References . . . . . . . . . . . . . . . . . . . . . . 194

7 Level-2 Trigger . . . . . . . . . . . . . . . . . . . . . . . 1957.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 1957.2 Level-2 Requirements for the Inner Detector. . . . . . . . . . . 1957.3 Performance of High-pT Triggers . . . . . . . . . . . . . . 196

7.3.1 Feature Extraction in the Precision Tracker. . . . . . . . . 1977.3.2 Feature Extraction in the TRT . . . . . . . . . . . . . 1987.3.3 Global Performance . . . . . . . . . . . . . . . . 202

7.4 B-physics Triggers. . . . . . . . . . . . . . . . . . . . 2057.4.1 B0

d → J/ψ K0s . . . . . . . . . . . . . . . . . . . . . . . 206

7.4.2 Inclusive D±s → φ π± . . . . . . . . . . . . . . . . . . . . 208

7.4.3 B0d → π+π- . . . . . . . . . . . . . . . . . . . . . . . . 209

7.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . 2107.6 References . . . . . . . . . . . . . . . . . . . . . . 210

8 Conclusions on Performance . . . . . . . . . . . . . . . . . . 2118.1 Satisfaction of Specifications . . . . . . . . . . . . . . . . 211

8.1.1 Basic Specifications . . . . . . . . . . . . . . . . . 2118.1.2 Triggering Specifications . . . . . . . . . . . . . . . 2128.1.3 Pattern Recognition Specifications . . . . . . . . . . . 2128.1.4 Physics Specifications . . . . . . . . . . . . . . . . 212

8.2 Work to Do . . . . . . . . . . . . . . . . . . . . . . 2138.3 Summary . . . . . . . . . . . . . . . . . . . . . . . 2148.4 References . . . . . . . . . . . . . . . . . . . . . . 214

9 Alignment . . . . . . . . . . . . . . . . . . . . . . . . 2159.1 Requirements . . . . . . . . . . . . . . . . . . . . . 215

9.1.1 Requirements for the TRT . . . . . . . . . . . . . . 2159.1.2 Requirements for the Pixels and SCT. . . . . . . . . . . 216

9.2 Alignment Strategy . . . . . . . . . . . . . . . . . . . 2199.2.1 Measurements of Prototype Structures . . . . . . . . . . 2199.2.2 Initial X-Ray Survey . . . . . . . . . . . . . . . . 2209.2.3 Geodetic Grids . . . . . . . . . . . . . . . . . . 2209.2.4 Track-Based Alignment Procedures . . . . . . . . . . . 220

9.3 Techniques . . . . . . . . . . . . . . . . . . . . . . 2219.3.1 Electronic Speckle Pattern Interferometry . . . . . . . . . 221

9.3.1.1 Introduction . . . . . . . . . . . . . . . . 2219.3.1.2 Experimental Method . . . . . . . . . . . . . 2229.3.1.3 Typical Examples of ESPI in the ATLAS SCT. . . . . 224


xiv Table Of Contents

9.3.2 Initial Survey with X-Rays . . . . . . . . . . . . . . 2259.3.2.1 SCT . . . . . . . . . . . . . . . . . . . 2259.3.2.2 X-Ray Source . . . . . . . . . . . . . . . . 2259.3.2.3 Measurement System . . . . . . . . . . . . . 2279.3.2.4 SCT X-ray Survey Accuracy. . . . . . . . . . . 228

9.3.3 Geodetic Grids . . . . . . . . . . . . . . . . . . 2299.3.3.1 Introduction . . . . . . . . . . . . . . . . 2299.3.3.2 Network Design. . . . . . . . . . . . . . . 2309.3.3.3 Barrel SCT and Pixel Alignment Networks . . . . . 2319.3.3.4 Forward SCT Alignment Networks . . . . . . . . 2329.3.3.5 Network Precision Calculations . . . . . . . . . 2329.3.3.6 Additional Requirements . . . . . . . . . . . 233

9.3.4 Frequency Scan Interferometry . . . . . . . . . . . . 2349.3.4.1 Introduction . . . . . . . . . . . . . . . . 2349.3.4.2 Basic Principles of FSI . . . . . . . . . . . . . 2349.3.4.3 Jewels . . . . . . . . . . . . . . . . . . 2369.3.4.4 Laboratory Test Results . . . . . . . . . . . . 237

9.3.5 Straightness Monitors . . . . . . . . . . . . . . . . 2389.3.5.1 Light Distribution System . . . . . . . . . . . 2389.3.5.2 Amorphous Silicon Strip Sensors . . . . . . . . . 2399.3.5.3 Integrated Readout Electronics . . . . . . . . . 2409.3.5.4 Test Results . . . . . . . . . . . . . . . . 241

9.3.6 Use of Tracks from Collisions . . . . . . . . . . . . . 2429.3.6.1 TRT Track Alignment . . . . . . . . . . . . . 2429.3.6.2 SCT/Pixel Track Alignment . . . . . . . . . . 242

9.4 References . . . . . . . . . . . . . . . . . . . . . . 243

A Members of the ATLAS Collaboration . . . . . . . . . . . . . . 245


Contents of Volume II xv

Contents of Volume II

10 The Pixel Detector System . . . . . . . . . . . . . . . . . . . 25710.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 25710.2 Physics Requirements and Layout . . . . . . . . . . . . . . 26110.3 Pixel Sensors. . . . . . . . . . . . . . . . . . . . . . 26510.4 Pixel Electronics . . . . . . . . . . . . . . . . . . . . 28110.5 Modules . . . . . . . . . . . . . . . . . . . . . . . 33310.6 Mechanics . . . . . . . . . . . . . . . . . . . . . . 34510.7 Project Organisation and Management . . . . . . . . . . . . 379

11 The Semiconductor Tracker . . . . . . . . . . . . . . . . . . 38511.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 38511.2 Global Issues . . . . . . . . . . . . . . . . . . . . . 38911.3 Detectors . . . . . . . . . . . . . . . . . . . . . . . 40111.4 Readout Electronics . . . . . . . . . . . . . . . . . . . 42711.5 Modules . . . . . . . . . . . . . . . . . . . . . . . 46311.6 Calibration and Monitoring . . . . . . . . . . . . . . . . 49311.7 Cooling . . . . . . . . . . . . . . . . . . . . . . . 49711.8 Support Structure . . . . . . . . . . . . . . . . . . . . 50911.9 Material Compilation. . . . . . . . . . . . . . . . . . . 53111.10 Module Construction. . . . . . . . . . . . . . . . . . . 53511.11 Assembly . . . . . . . . . . . . . . . . . . . . . . . 55511.12 Prototyping and System tests . . . . . . . . . . . . . . . . 56511.13 Project Management . . . . . . . . . . . . . . . . . . . 581

12 The Transition Radiation Tracker . . . . . . . . . . . . . . . . 59312.1 Overview . . . . . . . . . . . . . . . . . . . . . . . 59312.2 Basic Detector Properties and Performance . . . . . . . . . . . 61512.3 Detecting Elements . . . . . . . . . . . . . . . . . . . 65312.4 Design and Construction of the Barrel TRT . . . . . . . . . . . 66312.5 Design and Construction of the End-Cap TRT . . . . . . . . . . 69112.6 Quality Assurance at the Assembly Sites . . . . . . . . . . . . 73112.7 Assembly at CERN and Commissioning of the Detector. . . . . . . 74112.8 TRT Front-End Electronics . . . . . . . . . . . . . . . . . 74512.9 TRT Services. . . . . . . . . . . . . . . . . . . . . . 76712.10 Project Organisation and Management . . . . . . . . . . . . 809

13 Common Inner Detector Electronics . . . . . . . . . . . . . . . 81713.1 Overview . . . . . . . . . . . . . . . . . . . . . . . 81713.2 Radiation Damage. . . . . . . . . . . . . . . . . . . . 81913.3 Grounding and Power Supplies . . . . . . . . . . . . . . . 82313.4 Off-Detector Readout Electronics . . . . . . . . . . . . . . 82413.5 Detector Control System . . . . . . . . . . . . . . . . . 83913.6 References . . . . . . . . . . . . . . . . . . . . . . 858

14 Common Inner Detector Services . . . . . . . . . . . . . . . . 859


xvi Contents of Volume II

15 Installation, Operation and Maintenance . . . . . . . . . . . . . 86715.1 Assembly and Testing . . . . . . . . . . . . . . . . . . 86715.2 Installation of the Inner Detector into the Liquid Argon Cryostat . . . 86715.3 Access to the Inner Detector . . . . . . . . . . . . . . . . 86815.4 Operation and Running Costs . . . . . . . . . . . . . . . 869

16 Safety . . . . . . . . . . . . . . . . . . . . . . . . . . 87716.1 Introduction. . . . . . . . . . . . . . . . . . . . . . 87716.2 Mechanical Aspects . . . . . . . . . . . . . . . . . . . 87716.3 Cooling . . . . . . . . . . . . . . . . . . . . . . . 87816.4 Gases and Flammable Materials . . . . . . . . . . . . . . . 87916.5 Electrical and Electronics Aspects . . . . . . . . . . . . . . 88016.6 Alignment Procedures . . . . . . . . . . . . . . . . . . 88016.7 Radiation. . . . . . . . . . . . . . . . . . . . . . . 88216.8 References . . . . . . . . . . . . . . . . . . . . . . 882

A ATLAS Underground Area and Axis System . . . . . . . . . . . . 883

B Product Breakdown Structure . . . . . . . . . . . . . . . . . 885B.1 References . . . . . . . . . . . . . . . . . . . . . . 885

C Acronyms and abbreviations . . . . . . . . . . . . . . . . . . 893


1 Introduction 1

1 Colour Figures

Figure 1-i Three-dimensional view of the ATLAS Inner Detector (from the GEANT program).

Fo

rwar

d S

CT

Bar

rel S

CT

TR

T

Pix

el D

etec

tors


2 1 Introduction

Figure 1-ii Event display of the process H → ZZ∗ → μ+μ−e+e− in the barrel part of the Inner Detector.

ATLAS Barrel Inner DetectorH → ZZ* → μ+μ-e+e- ( mH = 130 GeV )

e+

e-

μ+

μ-


1 Introduction 3

1 Introduction

1.1 Purpose and Organisation of the Inner Detector TDR

This Technical Design Report describes the ATLAS Inner Detector (ID), which tracks chargedparticles from the LHC beam-pipe to the electromagnetic (EM) calorimeter system. In this chap-ter a brief overview of the ID is given, together with a discussion of project management issues,including the overall schedule and costs.

The following chapters deal with the overall performance of the ID.

Chapter 2 lists the performance specifications, the types of events used in the performance sim-ulations, and describes the technical aspects of the simulation code.

Chapter 3 describes the layout implemented into the simulation code in detail, including a dis-cussion of the magnetic field, the detector material, and the services. Sections 3.5, 3.1.2 and 3.7describe the simulation of each sub-system’s response.

Chapter 4 discusses the performance of the detector using single tracks to determine the basictransverse momentum, sign of charge, angular and impact parameter resolutions. Isolated sin-gle particles are considered first, and then the effect of pile-up from other events in the samebeam crossing is included. The electron identification performance using the transition-radia-tion signature is also described.

Chapter 5 contains details of the pattern recognition algorithms used to reconstruct complexevents. The quality of the algorithms is first evaluated using isolated high pT tracks with andwithout pile-up events. Tracks in jets are then studied, especially for jets containing B-hadrons,which are an important physics signature.

Chapter 6 then investigates some interesting benchmark physics processes, involving electronsignatures, b-tagging, photon identification, and V0 reconstruction. However, complete physicsanalyses do not form part of this TDR: they will be the subject of a separate volume which willdescribe the overall performance of ATLAS.

Chapter 7 discusses the use of the Inner Detector in the Level-2 trigger.

Chapter 8 completes the performance studies with a brief summary and conclusions.

Chapter 9 discusses alignment. The alignment system must link together all elements of the de-tector and its specifications are intended to ensure that the overall ID performance is not limitedby alignment errors. This chapter describes all aspects of this problem, including the initial sur-vey information, the alignment grids and the technologies used for their measurement, and theuse of track information for the final overall monitoring of the alignment stability.

The three sub-systems of the ID are then described in detail, including the status of the proto-typing work, and the test results upon which the design is based. These chapters form the bulkof the technical information. The description of the pixel system in Chapter 10 is preliminary,and a supplementary Technical Design Report is scheduled for April 1998 and will give the fulldescription of this sub-system. Chapter 11 covering the Semiconductor Tracker (SCT) and


4 1 Introduction

Chapter 12 covering the Transition Radiation Tracker (TRT) give complete descriptions of de-signs which should form the basis for construction approval.

Some common areas of the detector are then described in separate chapters. The common as-pects of the electronics are described in Chapter 13, which includes a description of the problemof radiation damage to the ID electronics and the methods used to overcome this difficulty.Chapter 14 concentrates on the overall integration of the detector, including a description of theservice routings to the outside of ATLAS. The installation plan, and means of access and repairare covered in Chapter 15. Since the integration design cannot be finalised before the sub-sys-tem design, the information presented in these chapters is less final than that in the sub-systemchapters. Where necessary a conservative approach has been adopted in order to ensure that afeasible solution is available. Work is still proceeding to develop more advanced solutions, withthe aim of reducing to an absolute minimum the passive material in the ID, and also to distrib-ute the material in such a way as to minimise its impact on both the tracking and on the calo-rimeter performance for physics. Finally Chapter 16 covers safety aspects of the Inner Detectorsystem.

1.2 Overview of the ATLAS Inner Detector

1.2.1 Physics Goals

The ATLAS Collaboration proposes to build a general-purpose pp detector which is designed toexploit the full discovery potential of the Large Hadron Collider (LHC).

The LHC offers a large range of physics opportunities, among which the origin of mass at theelectroweak scale is a major focus of interest for ATLAS. The detector optimisation is thereforeguided by physics issues such as sensitivity to the largest possible Higgs mass range. Other im-portant goals are the searches for heavy W- and Z-like objects, for supersymmetric particles, forcompositeness of the fundamental fermions, as well as the investigation of CP violation in B-de-cays, and detailed studies of the top quark. The ability to cope well with a broad variety of pos-sible physics processes is expected to maximise the detector’s potential for the discovery of new,unexpected physics.

Many of the interesting physics questions at the LHC require high luminosity, and so the prima-ry goal is to operate at a luminosity of 1034 cm-2s-1 with a detector that provides as many signa-tures as possible, using electron, photon, muon, jet, and missing transverse energymeasurements, as well as b-quark tagging. The variety of signatures is considered to be impor-tant in the high-rate environment of the LHC in order to achieve robust and redundant physicsmeasurements with the capability for internal cross-checks.

Emphasis is also put on the performance necessary for the physics accessible during the initiallower luminosity running (a few times 1033 cm-2s-1), using more complex signatures such asτ-lepton detection and heavy-flavour tags from secondary vertices.

Finally, the detector is conceived for assured performance even at the highest possible luminos-ities (in excess of 1034 cm-2s-1) which ultimately could be delivered by the LHC.


1 Introduction 5

The ATLAS detector concept meeting these requirements was first presented in the Letter of In-tent (LoI) [1-1] and the Technical Proposal [1-2]. The task of the Inner Detector (ID) is to recon-struct the tracks and vertices in the event with high efficiency, contributing, together with thecalorimeter and muon systems to the electron, photon and muon recognition, and supplyingthe important extra signature for short-lived particle decay vertices. Its acceptance covers thepseudo-rapidity region of ±2.5, matching that of the rest of the ATLAS systems for precisionmeasurements.

1.2.2 The Inner Detector Layout

A three-dimensional cutaway view of the layout of the Inner Detector is shown in Figure 1-i,and a cross-sectional view of one quarter of the detector is given in Figure 1-1. It combineshigh-resolution detectors at inner radii with continuous tracking elements at outer radii, all con-tained in a solenoidal magnet with a central field of 2T.

The momentum and vertex resolution targets require high-precision measurements to be madewith fine-granularity detectors given the very large track density expected at the LHC. Semi-conductor tracking (SCT) detectors, using silicon microstrip and pixel technology offer thesefeatures. Highest granularity around the vertex region is achieved using semiconductor pixeldetectors. However, the total number of precision layers must be limited because of the materialthey introduce, and because of their high cost. At least four strip layers and three pixel layersare therefore crossed by each track in this design. A large number of tracking points (typically36 per track) is given by a straw tube tracker (TRT) which provides the possibility of continuoustrack-following with much less material per point and at lower cost. The combination of the twotechniques gives very robust pattern recognition and high precision in both φ and z coordinates.The straw hits at the outer radius contribute to the momentum measurement, with the lowerprecision per point compared to the silicon being compensated by the large number of measure-ments and the higher average radius. The relative precisions of the different measurements arewell matched, so that no single measurement dominates the momentum resolution. This meansthat the overall performance is robust, even in the event that a single system does not performto its full specification. The high density of measurements in the outer part of the tracker is alsovaluable for the detection of V0 decays, which form a crucial part of the signature for CP viola-tion in the B system. In addition, the electron identification capabilities of the whole experimentare enhanced by the detection of transition-radiation photons in the straw tubes.

The outer radius of the tracker cavity is 115 cm, fixed by the inner dimension of the cryostatcontaining the liquid argon EM calorimeter, and the total length is 7 m, limited by the positionof the end-cap calorimetry. Mechanically, the Inner Detector consists of three units: a barrel partextending over ±80 cm, and two identical end-caps covering the rest of the cylindrical cavity.The precision tracking elements are contained within a radius of 56 cm, followed by the contin-uous tracking, and finally the general support and service area at the outermost radius. In orderto give uniform coverage over the full acceptance, the final TRT wheels at high z must extendinwards to a lower radius than the rest of that detector.

In the barrel, the high-precision detector layers are arranged on concentric cylinders around thebeam axis in the region with |η| < 1, while the end-cap detectors are mounted on disks perpen-dicular to the beam axis. The pixel layers are segmented in Rφ and z, while the silicon strips usesmall angle (40 mrad) stereo to measure both coordinates, with one set of strips in each layermeasuring φ. The barrel TRT straws are parallel to the beam direction. All the end-cap trackingelements are located in planes perpendicular to the beam axis. The strip detectors have one set


6 1 Introduction

✞ ✜

Figure 1-1 A cross-section of the ID engineering layout through the beam axis.


1 Introduction 7

of strips running in radial directions, and a set of stereo strips at an angle of 40 mrad. The con-tinuous tracking consists of radial straws arranged into wheels.

The basic design parameters and the resolutions for space-point measurements are summarisedin Table 1-1. The layout provides full tracking coverage over |η| ≤ 2.5, including impact pa-rameter measurements and vertexing for heavy-flavour and τ tagging. The secondary vertexmeasurement performance will be enhanced with an innermost additional layer of pixels, at aradius of about 4 cm, as close as is practical around the beam pipe. The lifetime of such a detec-tor will be limited by radiation damage, and would need replacement after a few years, the ex-act time depending on the luminosity profile. A large amount of interesting physics can be donewith this detector during the initial lower luminosity running, especially in the B sector, but re-cent physics studies have demonstrated the value of good b-tagging performance during allphases of the LHC, for example in Higgs and supersymmetry searches. It is therefore consid-ered as an option that the B-layer can be replaced to give the highest possible performancethroughout the Inner Detector lifetime. In this TDR, physics studies will be shown using the fullimpact parameter resolution expected with the B-layer present, and with the poorer perform-ance obtained in its absence. The mechanical design allows for the possibility of replacing theB-layer, and solutions are being investigated to achieve this with the minimum disturbance tothe rest of the Inner Detector. The cost of the initial B-layer is included in the estimates present-ed, but not the cost of any optional replacements. The exact lifetime of the layer will depend onthe time taken to accumulate integrated luminosity, but using a realistic model, the earliest datefor such a replacement is around 2009.

1.2.2.1 The Pixel Detector

The pixel detector is designed to provide a very high-granularity, high-precision set of measure-ments as close to the interaction point as possible. The system provides three of the precisionmeasurements over the full acceptance, and determines the impact parameter resolution andthe ability of the Inner Detector to find short-lived particles such as b-quarks and τ-leptons(Section 6.7). The two-dimensional segmentation of the sensors (Section 10.3) gives space pointswithout any of the ambiguities associated with projective geometries, but requires the use of ad-

Table 1-1 Parameters of the Inner Detector. The resolutions quoted are typical values (the actual resolution ineach detector depends on |η|).

System PositionArea(m2)

Resolutionσ (μm)

Channels(106)

η coverage

Pixels 1 removable barrel layer 0.2 Rφ = 12, z = 66 16 ±2.5

2 barrel layers 1.4 Rφ = 12, z = 66 81 ±1.7

4 end-cap diskson each side

0.7 Rφ = 12, R = 77 43 1.7-2.5

Silicon strips 4 barrel layers 34.4 Rφ = 16, z = 580 3.2 ±1.4

9 end-cap wheelson each side

26.7 Rφ = 16, R = 580 3.0 1.4–2.5

TRT Axial barrel straws 170 (per straw) 0.1 ±0.7

Radial end-cap straws 170 (per straw) 0.32 0.7–2.5

36 straws per track


8 1 Introduction

vanced electronic techniques and interconnections for the readout. The readout chips are oflarge area, with individual circuits for each pixel element, including buffering to store the datawhile awaiting the level-1 trigger decision (Section 10.4). Each chip must be bump bonded tothe detector substrate in order to achieve the required density of connections. In addition, thechips must be radiation hardened to withstand over 300 kGy of ionising radiation and over5⋅1014 neutrons per cm2 in ten years of operation (Section 10.4.10). The system offers 140 milliondetector elements, each 50 μm in the Rφ direction and 300 μm in z, which are invaluable for thetask of pattern recognition in the crowded environment of the LHC.

The system consists of three barrels at average radii of ~ 4 cm, 11 cm, and 14 cm, and four diskson each side, between radii of 11 and 20 cm, which complete the angular coverage. The systemis designed to be highly modular, containing approximately 1500 identical barrel modules and1000 identical disk modules, and uses only one type of support structure in the barrel and onetype in the disks (Section 10.6).

The pixel modules are very similar in design for the disks and barrels (Section 10.5). Each barrelmodule is 62.4 mm long and 22.4 mm wide, with 61440 pixel elements, read out by 16 chipseach serving an array of 24 by 160 pixels. The output signals are routed on the sensor surface toa hybrid on top of the chips, and from there to a separate clock and control integrated circuit.The modules are overlapped on the support structure in order to give hermetic coverage. Thethickness of each layer in the simulation is less than 1.39% of a radiation length.

A great deal of progress has been made in all the critical areas of this project, as is illustrated indetail in Chapter 10. However some technical issues remain open, and these are being ad-dressed by a collaborative R&D effort, according to a well-defined timescale. A demonstratorprogram has been launched, so that in about one year’s time, an “existence-proof” pixel mod-ule, meeting most of the LHC requirements, can be presented, together with the final detectordesign, in the pixel Technical Design Report.

1.2.2.2 The Semiconductor Tracker

The SCT system is designed to provide four precision measurements per track in the intermedi-ate radial range, contributing to the measurement of momentum, impact parameter and vertexposition, as well as providing good pattern recognition by the use of high granularity. The sys-tem is an order of magnitude larger in surface area than previous generations of silicon micros-trip detectors, and in addition must face radiation levels which will alter the fundamentalcharacteristics of the silicon wafers themselves (see Sections 11.2 and 11.3).

The barrel SCT uses four layers of silicon microstrip detectors to provide precision points in theRφ and z coordinates, using small angle stereo to obtain the z measurement. Each silicon detec-tor is 6.36 × 6.40 cm2 with 768 readout strips each with 80 μm pitch (Section 11.3). Each moduleconsists of four detectors. On each side of the module, two detectors are wire-bonded togetherto form 12.8 cm long strips. Two such detector pairs are then glued together back-to-back at a40 mrad angle, separated by a heat transport plate, and the electronics is mounted above the de-tectors on a hybrid (Section 11.5). The readout chain consists of a front-end amplifier and dis-criminator, followed by a binary pipeline which stores the hits above threshold until the firstlevel trigger decision (Section 11.4). The forward modules are very similar in construction butuse tapered strips, with one set aligned radially. Forward modules are made with both ~ 12 and7 cm lengths.


1 Introduction 9

The detector contains 61 m2 of silicon detectors, with 6.2 million readout channels. The spatialresolution is 16 μm in Rφ and 580 μm in z. Tracks can be distinguished if separated by morethan ~ 200 μm.

The barrel modules are mounted on local supports which allow units of six modules to be test-ed together before mounting on carbon-fibre cylinders which carry the cooling system; the fourcomplete barrels at radii of 300, 373, 447 and 520 mm are then linked together. The forwardmodules are mounted in up to three rings onto nine wheels, which are interconnected by aspace-frame. The radial range of each disk is adapted to limit the coverage to |η| ≤ 2.5 byequipping each one with the minimum number of rings, and by using 6 cm long moduleswhere appropriate (Section 11.8).

Solutions have been found to the critical issues in the system, and prototype modules have beensuccessfully tested in beams in a magnetic field, showing the required performance in resolu-tion, signal-to-noise and speed. Modules containing both front-end electronics and detectors, ir-radiated to the level expected for 10 years of LHC operation, have also been shown to functionwithin specifications (Section 11.3.4.10).

The system requires a very high dimensional stability, cold operation of the detectors, and theevacuation of the heat generated by the electronics and the detector leakage current. The struc-ture is therefore designed with materials with as low a coefficient of thermal expansion as possi-ble. The cooling is a bi-phase system using ice suspended in a methanol-water mixture (“binaryice”) to achieve low thermal gradients across the detector (Sections 11.7 and 11.8).

Final prototyping is now in progress, and the first pre-production modules (“module 0”) are ex-pected to be available in October 1998.

1.2.2.3 The Transition Radiation Tracker

The TRT is based on the use of straw detectors, which can operate at the very high rates neededby virtue of their small diameter and the isolation of the sense wires within individual gas enve-lopes. Electron identification capability is added by employing xenon gas to detect transi-tion-radiation photons created in a radiator between the straws. This technique is intrinsicallyradiation hard, and allows a large number of measurements, typically 36, to be made on everytrack at modest cost. However the detector must cope with a large occupancy and high count-ing rates at the LHC design luminosity.

Each straw is 4 mm in diameter, giving a fast response and good mechanical properties for amaximum straw length of 150 cm. The barrel contains about 50000 straws, each divided in twoat the centre in order to reduce the occupancy and read out at each end. The end-caps contain320000 radial straws, with the readout at the outer radius. The total number of electronic chan-nels is 420000. Each channel provides a drift-time measurement, giving a spatial resolution of170 μm per straw, and two independent thresholds. These allow the detector to discriminate be-tween tracking hits, which pass the lower threshold, and transition-radiation hits, which passthe higher (Section 12.2).

The barrel section is built of individual modules with between 329 and 793 axial straws each,covering the radial range from 56 to 107 cm (Section 12.4). The modularity was chosen as a com-promise between the ease of construction and maintenance, and the additional structural ele-ments involved. The first six radial layers are inactive over the central 80 cm of their length, in


10 1 Introduction

order to reduce their occupancy, while providing extra coverage of the crack between the barreland end-cap sections.

The two end-caps each consist of 18 wheels. The 14 wheels nearest the interaction point coverthe radial range from 64 to 103 cm, while the last four wheels extend to an inner radius of 48 cmin order to maintain a constant number of crossed straws over the full acceptance (Section 12.5).To avoid an unnecessary increase in the number of crossed straws at medium rapidity, wheels7 to 14 have half as many straws per cm in z as the other wheels.

A primary concern in the design of this sub-system has been to obtain good performance athigh occupancy and high counting rate. In the barrel, the rate of hits above the lower thresholdvaries with radius from 6 to 18 MHz, while in the end-caps the rate varies with z from 7 to19 MHz. The maximum rate of hits above the higher TR-threshold is 1 MHz. Within a singledrift-time bin, the occupancy is about one third of that in the entire straw active time window. Afast, low-noise preamplifier-shaper circuit with active baseline restoration has been developedto process the signals, using a radiation hard bipolar process (Section 12.8). Position accuraciesof about 170 μm have been achieved in tests at average straw counting rates of about 12 MHz(Section 12.2). At these rates, only about 70% of the straws give correct drift time measurementsbecause of shadowing effects, but the large number of straws per track guarantees a measure-ment accuracy of better than 50 μm averaged over all straws at the LHC design luminosity, in-cluding errors from alignment. Extensive tests have been carried out on various prototypes intest beams, with additional sources giving high counting rates, and in nuclear reactor neutronfluxes. These tests, taken together with the current best estimates of the rates expected at LHCfrom all sources, give confidence that the detector will offer good performance up to luminosi-ties well in excess of the LHC design value (Sections 3.7 and 12.2.4).

A good pattern recognition performance is assured by the continuous tracking. Within the radi-al space available, the straw spacing has been optimised for tracking at the expense of electronidentification, which would be improved by a greater path length through the radiator materialand fewer active straws. The distribution of the straws over the maximum possible path lengthalso enhances the pattern recognition performance, by reducing the effect of loopers and inter-actions which can saturate small regions of the detector (Section 12.1.1).

The TRT contributes to the accuracy of the momentum measurement in the Inner Detector byproviding a set of measurements roughly equivalent to a single point of 50 μm precision. It aidsthe pattern recognition by the addition of around 36 hits per track, and allows a simple and fastlevel-2 track trigger to be implemented. It allows the Inner Detector to reconstruct V0s whichare especially interesting in CP-violating B decays. In addition it provides additional discrimi-nation between electrons and hadrons, with a pion rejection varying with η between a factor of15 and 200 at 90% electron efficiency.

1.2.3 Summary of Performance

All tracks with |η|< 2.5 are measured with six precision space-points and about 36 straws, ex-cept for a slight degradation across the barrel to end-cap transition region. With the B-layerpresent, seven precision points are obtained. In Figure 1-2 the number of silicon elements tra-versed is plotted, giving one hit for each pixel layer (in this case including the B-layer), and twofor each strip layer (Rφ and stereo measurement). Hence the nominal seven space points aremade up of eleven measurements, in three pixel layers and four SCT layers. In Figure 1-3 thenumber of crossed straws in the TRT is plotted. In the end-cap TRT, a lower number of straws is


1 Introduction 11

used in some wheels in order to minimise the material and give the required number of hitswithout increased cost.

The momentum resolution of the Inner Detector is limited by several factors: the radial spaceavailable in the cavity, which limits the lever arm, the strength of the magnetic field, and the in-trinsic precision of the detector elements. The solenoid dimensions are constrained by thelength of the EM calorimeter cryostat with the result that the full length of the coil is only5300 mm. The magnetic field falls away from its central value of 2T along the z axis as shown inFigure 1-4, and the radial component increases strongly (Figure 1-5). In addition, above

Figure 1-2 Number of hits per track in the precisiondetectors.

Figure 1-3 Number of hits per track in the TRT.

Figure 1-4 The magnetic field strength in the beamdirection as a function of R and z.

Figure 1-5 The radial component of the magneticfield as a function of R and z.

0

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12 1 Introduction

|η| = 1.85, tracks leave the Inner Detector volume before reaching the maximum radius of thecavity, thereby reducing the field integral available as compared to the lower |η| regions. Theseeffects limit the momentum resolution achievable in the end-cap regions, especially for |η| > 2.The full momentum resolution, combining the information from the discrete precision pointsand the large number of drift-time measurements of the TRT in a global fit through the realisticsolenoid field map, is shown in Figure 1-6 (see Section 4.1). This resolution is sufficient to iden-tify the charge sign of particles up to the highest energies expected at LHC, for example fromthe decays of new vector bosons in the TeV mass range, allowing the parity violating asym-metries to be investigated (see Section 4.2). Most studies in this TDR do not use the full magnet-ic field map, since the tracking algorithms are currently designed to use a uniform field. Theonly significant effect of the non-uniform field is on the momentum resolution at high η.

Figure 1-ii shows an example of the use of theID in the search for the Higgs boson. The de-cay H → ZZ* → e+e-μ+μ- was simulated to-gether with the expected pile-up at the LHCdesign luminosity, for a Higgs mass (mH) of130 GeV. A search was then performed for alltracks with transverse momenta above 5 GeV.In spite of the occupancy created by loopingtracks and hits from secondary interactions,the pattern recognition successfully identifiedthe four high-pT lepton tracks. The recon-structed tracks are plotted in red. No falsetracks were found. The display illustratesclearly how the high-pT tracks can be pickedout even by eye using the continuous trackingin the straw tubes. However, the high preci-sion of the SCT and pixel layers is less easilyvisualised: in these devices the high granulari-ty (and hence low occupancy) combined withthe very high spatial precision also gives ex-cellent track finding ability, and together thesecomplementary technologies give an extremely robust performance (see Chapter 5). The muontracks can be identified using the toroid spectrometer, while the electron tracks can be identifiedusing energy-momentum matching with the EM calorimeter. In addition, the transition-radia-tion performance is illustrated in this event. The e- track has nine hits with energies above thetransition-radiation discriminator threshold (plotted in red), while the neighbouring μ+ hasonly two such hits. This additional signature enhances the overall electron identification per-formance (see Sections 6.1 and 6.2).

A crucial parameter for the physics performance of the ID is the resolution on the impact pa-rameters of tracks from secondary vertices. The impact parameter resolution can be parame-trised in Rφ as σ(d0) = 11 ⊕ 60/pT √sinθ and in z as σ(z0) = 70 ⊕ 100/pT √sin3θ (in μm) with thededicated B-physics layer of pixels present at 4 cm radius. The full simulation of this perform-ance for different track transverse momenta is shown in Figure 1-7 and Figure 1-8. During theinitial low luminosity running, B-physics studies will concentrate on CP-violating channels inthe B-system. In addition, the ability to tag jets containing b-quarks will be used in Higgs andsupersymmetry searches up to the highest luminosities.

Figure 1-6 The Inner Detector momentum resolutionwith beam constraint, for tracks with pT = 500 GeV, forthe real solenoidal field compared to a uniform 2T field.

0

0.25

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0 0.5 1 1.5 2 2.5

|η|

σ(1/

p T)

(TeV

-1)


1 Introduction 13

The ID has excellent pattern recognition properties, with an efficiency of above 99% for findingmuons with pT = 20 GeV, even in the presence of the pile-up expected at design luminosity.Tracks have also been studied in jets, for example from H → bb with mH = 400 GeV. An efficien-cy of ∼ 90% can be obtained for tracks with pT > 1 GeV, with cuts which ensure that the fractionof fake tracks anywhere in the acceptance remains below ∼ 0.5% (see Section 5.2.3).

1.2.4 Material Budget

In many previous tracking detectors, electrons could be drifted over large distances in gaseousdetectors, and signals could be transmitted along silicon strip detectors, thus placing the elec-tronics outside of the active tracking volume. The high rates at LHC make this impossible overthe acceptance of the ATLAS system. Instead, the tracking detectors must be designed withtheir electronics in close proximity to the active elements. This inevitably leads to a significantamount of material being placed in the tracking volume, from the electronics itself, and its serv-ices, such as power cabling, cooling and monitoring cabling. In addition, the high momenta ofthe tracks necessitate a very high level of precision in the detector, and so the support structurerequires mechanical stability at the level of a few tens of microns over distances of metres. Thisrequirement can only be met by a rigid structure which inevitably increases the material budg-et.

Every effort has been made to keep the material in the tracking volume to a minimum, by care-ful design of the active detectors and by the use of low-Z materials (such as aluminium for thepower cables, and carbon-fibre reinforced plastic for the support structures). The distribution ofmaterial, in radiation lengths, as a function of |η| is shown in Figure 1-9. The level correspondsto an average of 43% X0 with a peak at ~ 60%.

The effect of the material can be seen in various performance studies. Most of these studies havebeen performed including the dedicated B-layer. For example, photons can convert inside theID, and so reduce the signal for the channel H→γγ by creating tails in the energy measurement.Careful studies, using the ID to reconstruct conversions wherever possible, show that the mate-

Figure 1-7 Transverse impact parameter resolutionas a function of pT for η=0.

Figure 1-8 Longitudinal impact parameter resolutionas a function of pT for η=0.

0

50

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(μm

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σ(z 0)

(μm

)


14 1 Introduction

rial causes an additional loss of 3.8% of the signal outside of a mass bin of ± 1.4 σ centred on thepeak [1-4]. Since 80% of the signal remains inside the bin, this loss is considered to be tolerable.85% of converted photons with high pT are reconstructed by the ID (Section 6.3). Those photonswhich are not reconstructed have mostly converted at large radius, and their energies are there-fore still well measured in the calorimeter.

The material has a similar effect on electrons,provoking bremsstrahlung and affecting boththe energy measurement in the calorimeterand the track momentum measurement, andhence the energy-momentum matching usedfor electron identification (Section 6.1). An ex-ample of this effect was studied in [1-4] for thechannel H → eeee, with a Higgs mass of130 GeV. The overall reconstruction efficiencywas 89%, but only 85% of the events lie within±2σ of the mass peak. The tails in the mass dis-tribution are increased by the effect of theID material, with the material at small radiushaving the largest impact, but once again theeffect on the physics reach is tolerable.

Because low-Z materials are used, the ratio ofinteraction length to radiation length is rela-tively high. This causes a loss of efficiency forhadrons, especially at low momentum, andscattering also degrades the impact parameterresolution. The efficiency for reconstructingpions with 1 GeV of pT falls as low as 87% inthe worst region (see Section 5.1.1). After cuts,within b-jets, 31% of the tails in the impact pa-rameter distribution are due to interactions inthe material of the detector, mostly from photon conversions, but also from nuclear interactions(see Section 5.2.2). In spite of this, a rejection of 80 is obtained against light quark jets and 40against gluon jets, while retaining an efficiency for tagging b jets of 50%, which is sufficient tomaintain the good physics performance (see Section 6.7.6).

In all of these examples, the effect of the material can be clearly identified in the ATLAS per-formance, but it does not create unacceptable problems for physics studies. However less mate-rial would clearly be of great benefit in many areas, if this can be achieved withoutcompromising the detector in other ways. Work is in progress to attempt to reduce the materialbudget still further, by detailed optimisation of the active detectors, and by further integrationof the overall support structure. Solutions involving more exotic materials such as carbon-car-bon composites or beryllium may be used in the pixel system, but would have serious cost im-plications if adopted throughout the ID. Studies are also underway to determine whetheradequate performance can be demonstrated with a layout with one less precision layer. Thiswould have the benefit of removing material at small radius where the effect on the calorimeterand tracking performance is greatest, although in all cases the innermost B-layer would be re-tained. These studies will be completed during 1997.

Figure 1-9 The amount of material in radiationlengths in the Inner Detector, including the B-layer asa function of η. The successive curves show thecumulative material in the pixel, SCT and TRT activevolumes. The final curve includes the material associ-ated with the Inner Detector, mainly due to services,which is outside the sensitive tracking volume butinside the electromagnetic calorimeter cryostat.

0

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1 Introduction 15

1.2.5 Evolution of the Layout since the Technical Proposal

At the time of the ATLAS Technical Proposal in 1994, the baseline tracker concept had alreadybeen decided, with the same complementary sub-systems of pixels, precision hits and TRT con-tinuous tracking as presented above. However, the technology for the precision hits in the for-ward region was not decided, and two options were presented: a baseline containingmicro-strip gas chambers (MSGCs), and an alternative using silicon detectors. Following theTechnical Proposal, these two options were further evaluated in terms of performance, ease ofconstruction and operation, and cost. An internal review concluded that there were benefitsfrom the use of the silicon technology, which was more mature and offered a higher intrinsicresolution, which outweighed the potential cost advantage of the MSGC option. In addition, thedetector was simplified by the use of a single technology.

More recently, a review in December 1996 evaluated progress with GaAs detectors as a radia-tion-hard alternative to silicon. These detectors had been included in the Technical Proposal de-sign in the most irradiated regions. Early results had indicated that the tolerance of GaAsdetectors to neutron irradiation was higher than that of silicon. However further studiesshowed that damage from charged particles was significant for these detectors, and it was con-cluded that GaAs detectors could not be guaranteed to provide a solution for the highest doseregions of the ID. On the other hand, improvements in understanding of the radiation damagein silicon had allowed a silicon solution to be designed that had a realistic chance of operatingfor the detector lifetime, albeit near the limit of current technology.

For these reasons, the design presented here consists of a unified silicon strip detector in the in-termediate radial range between the pixel detector and the TRT.

Finally, the choice of technology for the B-layer was left open in the Technical Proposal. A sili-con strip option was available, as well as the pixel option which was finally adopted. The pixeldesign was considered by an internal review to have a better prospect of providing the requiredphysics performance throughout the detector lifetime.

1.2.6 Radiation Environment

The radiation levels in the Inner Detector cavity will be extremely high, leading to damage inboth the silicon detectors and the electronics. The most relevant quantity for the damage in sili-con detectors is the fluence expressed in terms of 1 MeV equivalent neutrons. This is shown inFigure 1-iii. The instantaneous fluence of charged hadrons is shown in Figure 1-iv. Some valuesof the neutron fluences and dose accumulated annually in the detector are given in Table 1-2.

Table 1-2 Annual radiation doses in the Inner Detector at the LHC design luminosity.

1 MeV equivalent neutron fluence1013 cm-2/year

Ionising dosekGy/year

Position Typical value Maximum value Typical value Maximum value

Pixel detector 5 50 30 300

SCT 1.5 2 4 10

TRT 0.7 1 2 6


16 1 Introduction

For each system, a typical value is given as well as the highest value expected. For example, inthe pixel detector, the typical value is quoted for the 11 cm layer, and the highest value for inner-most B-layer.

These high radiation doses give rise to several problems for the Inner Detector: the silicon detec-tors themselves are affected, the electronics performance is degraded, and the particles contrib-ute background hits in the sensitive elements. The level of radiation is affected by the exactmaterials in the system. In the case of the Inner Detector, the presence of the TRT radiator andspecially installed polythene disks on the end-cap calorimeters reduces the energy of neutronsin the cavity and helps to reduce the damage they cause. All materials used in the Inner Detec-tor cavity must be qualified to survive the doses and fluences expected at the positions at whichthey are placed.

The problem of radiation damage to silicon detectors has been the subject of a large R&D pro-gramme, and it is now possible to describe the behaviour of the detectors in some detail up tofluences of 1015 1 MeV equivalent neutrons per cm2 (Sections 10.3 and 11.3). The depletion volt-age rises with increasing dose, and the operation of the detectors is limited by the maximumvoltage which can be applied without provoking breakdown. If the operating voltage is too lowto deplete the detector, the signal from the undepleted region is lost. The effect of radiationdamage is strongly temperature dependent, with both beneficial annealing effects, in which thedamage is recovered with time, and also “reverse annealing” which leads to an increase in thedepletion voltage with time. This effect can be removed if the detector is operated at low tem-perature: -5 to -10°C has been chosen as nominal (-7°C average in the SCT). This operating tem-perature also has the beneficial effect of reducing the leakage current and hence heat generationinside the detector substrate.

Low-temperature operation leads to significant operational problems. The entire silicon systemmust be enclosed in a cold envelope, with an active shield preventing heat transfer from theTRT. Access to the detector should be made with the minimum warming of the detector. A sce-nario has been developed in which the envelope is kept cold during access by a flow of cold drynitrogen, which also prevents condensation from developing. The detector can be moved to arefrigerated surface building on a transport frame equipped with such a supply of cold nitro-gen, and then dismantled in controlled conditions. Fortunately, the reverse annealing effect,which releases accumulated damage, is of little importance during the initial running periodwhen the total dose is small, and so warm-up during the first phase of operation is not a majorconcern.

In order to maintain good performance, all the electronics in the Inner Detector cavity will bepurchased from vendors using recognised radiation-hard chip fabrication processes. Such chipsare normally qualified to doses up to 10-100 kGy by the manufacturers, but tests have shownthat the radiation damage effects tend to saturate, and that the chips continue to operate wellabove the level guaranteed. All of the chips used in the Inner Detector cavity have been, or willbe, tested to doses exceeding those expected for 10 years of LHC operation (300 kGy in the pixelsystem), and two different processes will be prototyped. Test-beam studies have already beenperformed using prototypes containing such chips with satisfactory results (Sections 10.4, 11.4,and 12.8).

Finally the backgrounds in the detector from soft particles (mainly neutrons and photons) havebeen studied, for example by exposing straws to the neutron flux in a nuclear reactor. In all cas-es the hit rates expected are well below those from tracks from the primary interactions.


1 Introduction 17

1.3 Project Management, Schedule and Cost

1.3.1 Project Organisation

The Inner Detector sub-systems are each organised following the normal ATLAS structure. AProject Leader organises the execution of the project, aided by a Steering Group which containsrelevant technical expertise. Open working group meetings are held as necessary to performstudies and to work on the detailed detector design. The Project Leader maintains a project plancovering costs and responsibilities which is approved by an Institute Board, containing all theparticipating groups. Wherever possible, decisions are reached by consensus, but if needed avote can be taken with each Institute carrying one vote.

In the case of the pixel and TRT sub-systems, the number of participating institutes is sufficient-ly small for the functions of the Steering Group and Institute Board to be combined into onebody. This is not the case for the SCT, where the two bodies meet separately (Sections 10.7, 11.13and 12.10).

The overall coherence of the ID design is maintained by the ID Project Leader, supported by theID Steering Group (IDSG). The IDSG includes the project leaders of the sub-systems, theID project engineer, the ID co-ordinators for software, test-beam activities, performance studiesand electronics, and two additional members from each sub-system. The meetings are also at-tended by representatives of the Technical Co-ordination team. Overall ID issues are discussedat the ID Working Group meetings. On rare occasions, when major decisions affecting the ID aremade, the ID Institutes meet with the possibility of voting on the usual one-per-group basis.

The ID Project Leader and two other members of the IDSG are nominated by the ID communityas members of the ATLAS Executive Board, maintaining contact with the other ATLAS systems,and reporting to the ATLAS management and Spokesperson. The ID Project Leader worksclosely with the ATLAS Technical Co-ordinator on detector integration issues, and with the Re-sources Co-ordinator on financial issues. Regular reports on the progress of the ID are given inthe ATLAS Plenary Meetings, and discussed by the Collaboration Board as appropriate.

The current members of the Inner Detector Steering Group are:

G. Bachy Technical Co-ordination

P. Delpierre Pixel Representative

D. Froidevaux TRT Project Leader

M. Gilchriese Pixel Representative

A. Grillo SCT Representative

S. Haywood Inner Detector Performance Co-ordinator

H. Ogren TRT Representative

J. Pater Inner Detector Software Co-ordinator

M.A. Parker Inner Detector Project Leader

A. Romaniouk TRT Representative

L. Rossi Pixel Project Leader


18 1 Introduction

S. Stapnes Inner Detector Test-beam Co-ordinator

G. Tappern Inner Detector Project Engineer

M. Tyndel SCT Project Leader

Y. Unno SCT Representative

H.H. Williams Front-End Electronics Co-ordinator

Ex officio: ATLAS Management

1.3.2 Overall Schedule and Milestones

Detailed time schedules for each sub-system of the ID are given in the respective sub-systemchapters. Figure 1-10 shows the overall summary schedule for the whole detector. In order forthe detector to be ready for full operation in mid-2005, the detector installation inside the liquidargon cryostat of the EM calorimeter must begin in the second quarter of 2004, with cablingcomplete by the fourth quarter of 2004, leaving nine months for final testing and commission-ing. Given the complexity of the detector, a six-month period has also been foreseen before in-stallation begins, during which time the fully assembled detector will be tested in the surfaceassembly area. This procedure should minimise the risk of delays in the final testing phase,

Figure 1-10 The overall ID construction schedule.

ID Task Name1 Pixel TDR

2 Pixel module construction

3 Pixel barrel assembly and test

4 ID TDR

5 Detectors, barrel and forward

6 Front end electronics SCT

7 Silicon modules barrel and forward assembly

8 Assembly and testing SCT barrels

9 Assembly and testing SCT forward

10 Transport silicon barrel to Atlas site

11 Silicon barrel detector test & survey

12 TRT barrel construction

13 Barrel TRT assembled and tested

14 Assy silicon barrels to TRT and test

15 Assemble pixels to silicon barrel

16 Test and survey barrel detector

17 TRT forward construction

18 Forward TRT assembled and tested

19 Transport to Atlas site

20 Forward silicon test & survey

21 Assemble Forward silicon to TRT

22 Test and survey Forward region

23 Assemble Forward region to Barrel

24 Test Tracker on surface

25 Install Inner Detector services in ATLAS

26 Install Barrel in Atlas test and survey

27 Install Forward in Atlas test and survey

28 Inner Tracker commission

29 First Physics

1997 1998 1999 2000 2001 2002 2003 2004 2005 2006


1 Introduction 19

when access to the detector will be restricted and the working environment in the pit will be dif-ficult. All the elements of the ID must therefore be assembled by the fourth quarter of 2003. Thisconstrains the construction schedule of the sub-systems.

1.3.3 Quality Assurance and Quality Control

A quality assurance plan has been defined by the ATLAS Technical Coordination team for thewhole ATLAS project [1-5]. It is based on the recommendations stated in the ISO 9001 qualitysystems, but does not require that all participating groups are qualified at this standard. Prepa-rations have begun to follow the main recommendations, and a complete plan will be ready foreach sub-system in time for the construction of “module zero”, and the overall final design.

The plan requires

• design complying with standards (ISO, ASME, etc.), and design reviews;

• approval of drawings at the appropriate managerial level;

• documentation (to become embedded in the Engineering Data Management System);

• selection and radiation hardness testing of critically exposed components;

• traceability of all components;

• quality of processing, assembly, and handling (clean rooms, ...);

• acceptance tests before shipping and upon receipt at CERN.

Table 1-3 List of milestones of the ID construction.

Milestone Date

TRT end-cap module 0 December 1997

Pixel TDR April 1998

TRT barrel module 0 December 1998

SCT module 0 October 1998

Pixel module 0 June 1999

SCT barrel construction complete September 2002

SCT forward construction complete October 2002

TRT barrel construction complete December 2002

TRT end-cap construction complete February 2003

Pixel detector complete May 2003

Begin testing complete ID on surface September 2003

Start installation into ATLAS March 2004

Begin commissioning September 2004

First physics July 2005


20 1 Introduction

An Engineering Data Base Management System (EDMS) is currently being evaluated, with theintention that all relevant engineering data can be handled in a distributed way, facilitating themanagement of the project. The design and level of quality control are furthermore adapted tothe level of access for maintenance and repair which is foreseeable during the LHC operation.Access to the silicon detectors must be severely restricted, since any warm-up of these detectorswill greatly increase the damage from irradiation. A scenario for cold access has been devel-oped, but can only be used during a long annual shutdown. Access during shorter openings ofthe ATLAS detector will only allow minor interventions on cabling and patch panels.

1.3.4 Costs and Resources

The overall cost ceiling of the ATLAS detector has been set to 475 MCHF at 1995 prices. The col-laboration has agreed on cost ceilings for each system, with the ID maximum cost set to78.2 MCHF. The costs of the detector were presented to the LHCC cost review committee in Jan-uary 1997 (ATLAS Cost Planning Version 6, 31 January 1997). The detailed costings can befound in that document, and a summary of the main items is presented in Table 1-4. These costsinclude all items in the design, including the losses to be expected during production, and arebased on industrial quotes wherever possible, and on the most realistic market survey availablein other cases. A total of approximately 2000 staff years is anticipated to be used in the partici-pating institutes, which is not included in these costs. The cost of the B-layer is included in the

Table 1-4 Inner Detector cost summary (CORE units).

System Subtotal Costs (kCHF) Total Costs (kCHF)

Pixel detectors 1602

Pixel electronic modules and readout 10826

Pixel mechanics 1497

Pixel Total 13925

SCT detectors 20657

SCT electronic modules and readout 17082

SCT mechanics 4921

SCT Total 42660

TRT barrel mechanics 1789

TRT end-cap mechanics 6604

TRT electronics 6907

TRT infrastructure 700

TRT Total 16000

General ID items 5750

ID Total 78335


1 Introduction 21

total cost of the pixel system, but no provision is made for a replacement for this layer after itsperformance deteriorates from radiation damage.

The resources requested by the ID community from the national funding agencies were present-ed to the ATLAS Resources Review Board in the Interim Memorandum of Understanding (AT-LAS RRB-D 96-9, 19 March 1996). The final level of resources will only be known when the finalMemorandum of Understanding is signed. At present the expected resources are matched tothe anticipated costs. The ID community has a considerable strength, with 60 institutes involvedfrom 17 countries. The planned distribution of responsibilities for different tasks among the par-ticipating institutes can be found in the relevant sub-system chapters.

1.4 References

1-1 ATLAS Letter of Intent for a General-Purpose pp Experiment at the Large HadronCollider at CERN, CERN/LHCC/92–4, LHCC/I2 (1992).

1-2 The ATLAS Technical Proposal for a General Purpose pp Experiment at the Large HadronCollider at CERN, CERN/LHCC/94–43 (1994).

1-3 D. Froidevaux and A. Parker, ATLAS Internal Note, INDET-NO-046 (1994).

1-4 ATLAS Calorimeter Performance Technical Design Report,CERN/LHCC 96-40 (1996).

1-5 ATL-GE-CERN-QAP-0100 and references therein.


22 1 Introduction


1 Introduction 23

Z(c

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24 1 Introduction

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2 Introduction to the Performance 25

2 Colour Figures

Figure 2-i Display of simulated event in the ATLAS barrel Inner Detector, at low luminosity. Pre-cision hits are shown for 0 < η < 0.7; TRT hits are shown in barrel for z > 0; high threshold transition radiationhits are shown as red points. Fitted tracks (red), with pT > 0.5 GeV and 0 < η < 0.7, are shown just in the preci-sion tracker so as not to obscure the TRT hits.

Bd0

J ψ⁄ Ks0→

ATLAS Barrel Inner DetectorBd

o → J/ψ Kso

e-

e+

π-

π+


26 2 Introduction to the Performance

Figure 2-ii Display of simulated H → ZZ∗ → e+e−e+e− event (mH = 130 GeV) in the ATLAS barrel Inner Detec-tor, at the design luminosity of 1034 cm-2s-1. Precision hits are shown for 0 < η < 0.7; TRT hits are shown in bar-rel for z > 0; high threshold transition radiation hits are shown as red points. Fitted tracks (red), with pT > 5 GeVand 0 < η < 0.7, are shown just in the precision tracker so as not to obscure the TRT hits.

ATLAS Barrel Inner DetectorH → ZZ* → e+e-e+e- ( mH = 130 GeV )

e+

e-

e+

e-


2 Introduction to the Performance 27

Figure 2-iii Display of simulated H → bb event (mH = 400 GeV) in the ATLAS barrel Inner Detector. The lowerfigure is at low luminosity; the upper figure is at the design luminosity of 1034 cm-2s-1. Precision hits are shownfor 0 < η < 0.7; TRT hits are shown in barrel for z > 0. Fitted tracks (red), with pT > 1 GeV and 0 < η < 0.7, areshown just in the precision tracker so as not to obscure the TRT hits.

AT

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28 2 Introduction to the Performance


2 Introduction to Performance 29

2 Introduction to Performance

The layout and general requirements of the ATLAS Inner Detector are set out in the first chapterof this volume, with more details in the second volume [2-1]. In the following chapters(Chapters 2 to 8), the results of software simulation of the physics performance of the detectorare presented.

2.1 Overview

In Chapter 3, it is explained how the various subdetectors of the Inner Detector were simulatedand the immediate consequences of that in terms of the performance of those subdetectors isgiven.

In Chapter 4, the expected performance for single charged particles is presented. This demon-strates the intrinsic and optimal performance which can be expected from the Inner Detector.

In Chapter 5, pattern recognition is studied for single tracks, including the presence of pile-up,and for tracks in jets. This provides a realistic estimate of the performance which can be expect-ed.

In Chapter 6, the consequences of the performance of the Inner Detector are examined for ele-mentary physics studies. In some of these, use is made implicitly or explicitly of the ATLAS cal-orimeters, the performance of which are described in the corresponding TDR [2-2]. Thesestudies are components of more extensive physics analyses.

In Chapter 7, results from preliminary studies for the Level-2 Trigger using the Inner Detectorare given. While the Inner Detector undoubtedly will play an important role in the Trigger, andindeed some of the specifications placed on it relate to its performance in the context of trigger-ing, the design of the Level-2 Trigger is still in progress and consequently there is some uncer-tainty as to how algorithms will be implemented and the exact performance which can beexpected. More detailed results will be given in a Level-2 Trigger document to be submitted at alater stage.

The emphasis in the performance chapters of this volume (2 to 8) will be to compare the expect-ed performance of the Inner Detector with the specifications set out by the Inner Detector com-munity. It will not consider:

• Layout and detector optimisation - this has been considered in numerous working meet-ings and Inner Detector Notes.

• Radiation doses - discussed in Section 1.2.6.

• Alignment - discussed in Chapter 9.

Unless explicitly stated, all the work contained in this report corresponds to new studies. Thesehave used the simulation model, described in Chapter 3, which represents the design describedin this TDR.


30 2 Introduction to Performance

2.2 Definitions and Nomenclature

Coordinate systemAlong with Cartesian coordinates, cylindrical coordinates are also used: , θ and φ.Also used is the dip-angle: λ ≡ 90°-θ.

Helix fit parametersAll quantities are measured at the point of closest approach to x=0, y=0.In the x-y plane, the fitted parameters are:

• 1/pT - the reciprocal of the transverse1 momentum,

• φ - where tanφ ≡ py/px ,

• d0 - the transverse distance to the axis x=0, y=0; signed according to the reconstructed an-gular momentum of the track about the axis.

In the R-z plane, the fitted parameters are:

• cotθ = tanλ ≡ pz/pT ,

• z0 - the z position of the track at this point.

Particle separationAngular separations in 3-D are expressed in terms of , where Δη is the separa-tion in pseudorapidity.

2.3 Performance Specifications

The performance specifications were set out three years ago [2-3]. These were based on prelimi-nary studies of key physics topics, but also with an eye as to what might be expected from atracking detector. The appropriate physics processes were identified; appropriate definitionsmade and numerical limits were set. Since it was difficult to carry out complete physics analy-ses, it was possible to focus only on components of a problem and the setting of the specifica-tions was somewhat subjective. Although some of the specifications have been found to beincomplete (for example, the lack of definition of what is a fake track, which needs to be definedin the context in which it is used), they have provided useful guidance in assessing whether theproposed detector is adequate. In the studies presented in subsequent sections of this report, as-pects requiring more careful explanation are described in the appropriate detail.

The specifications are listed below. Unless otherwise stated, they are intended to be valid forboth low and high luminosity running.

2.3.1 Basic Specifications

Angular coverage

Tracking over the pseudorapidity range|η| ≤ 2.5:

1. With respect to the beam axis.

R x2

y2

+≡

ΔR Δη2 Δφ2+≡



• Number of precision measurements ≥ 5 for |η| ≤ 2.5 - implicitly, these should bespace-points (B1).

• Number of straw hits ≥ 36 for |η| ≤ 2.5, but allowed to fall to 25 in the overlap and at|η| ~ 2.5 (B2).

Precision in bending plane

• Momentum resolution pT×σ(1/pT) < 0.3 at pT = 500 GeV for |η| ≤ 2 and < 0.5 at|η| = 2.5 (B3).

• There is no explicit specification for impact parameter resolution, but clearly it should beas good as possible.

Precision in non-bending plane

• Polar angle resolution σ(θ) ≤ 2 mrad (B4).

Primary vertex

• Resolution of primary vertex with at least four charged tracks σ(z) < 1 mm (B5).

2.3.2 Pattern Recognition Specifications

Pattern recognition

• Efficiency for reconstructing an isolated track with pT ≥ 5 GeV should be ≥ 95%, with afake rate ≤ 1% of signal rates (R1).

• Efficiency for reconstructing all tracks with pT ≥ 1 GeV, in a cone of ΔR ≤ 0.25 around ahigh-pT isolated track, should be ≥ 90%, with a fraction ≤ 10% of such tracks being fakes(R2).

• At low luminosity, efficiency for reconstructing all tracks with pT ≥ 0.5 GeV from the pri-mary vertex and short-lived secondaries should be ≥ 95% (R3).

The requirements of the Level-2 Trigger are set out in the corresponding chapter, Chapter 7.

2.3.3 Physics Specifications

Electron identification

• Efficiency for reconstructing electrons pT ≥ 7 GeV, including the trigger efficiency and al-lowing for the effects of bremsstrahlung, should be ≥ 90% (P1).

• Efficiency for reconstructing secondary electrons with pT ≥ 0.5 GeV, near high-pT electroncandidates, and averaged over pT, should be ≥ 90% (P2).

• At low luminosity, efficiency for reconstructing electrons with pT ≥ 1 GeV should be≥ 70% (P3).

Photon identification

• Combined efficiency of the EM calorimeter and Inner Detector for identifying photons≥ 85%, with an electron rejection ≥ 500 (Z → e+e− background to H → γγ) and an isolatedπ0 rejection ≥ 3 (γ/π0 identification) (P4).



V0 identification

• At low luminosity, efficiency for reconstructing with pT ~ 5 GeV and decaying withR ≤ 50 cm should be ≥ 90% (P5).

Secondary vertices

• Ability to reconstruct accurately secondary vertices from b-decays (P6).

Vertex b-tagging

• Efficiency for tagging b-jets (by displaced vertex) ≥ 40%, with a rejection of non-b hadron-ic jets ≥ 50 (h, and SUSY particle searches) (P7).

• At low luminosity (with the B-layer), efficiency for tagging b-jets ≥ 50%, with a rejectionof non-b hadronic jets ≥ 50 (P8).

2.4 Simulation of Physics

Unless otherwise stated, all processes have been simulated with a collision point described bya Gaussian distribution in x, y and z, with σx = σy = 15 μm and σz = 5.6 cm. Since the simulationdoes not track particles whose lifetimes are not measurable, all ‘stable’ particles produced in aproper time less than O(1μm)/c are associated with the primary vertex, which is at the collisionpoint.

To understand the various performance aspects of the detector, the most appropriate physicsprocesses have been studied. While many specific processes have been used, four are used ex-tensively in the work discussed in this report.

2.4.1 B-meson Decays

Decays of B-mesons provide valuable information on the CKM matrix and, in particular, CP vi-olation. The reconstruction of B decays necessitates various studies of analysis ‘building blocks’such as soft-electron identification, V0 and secondary vertex reconstruction - these, along withthe reconstruction of exclusive decays, are discussed in Chapter 6. The B-meson lifetimes havebeen taken from the Particle Data Book [2-4] (with cτ around 450-460 μm for B0,±). An exampleof a B decay is shown in Colour Figure 2-i.

2.4.2 Single Particles

The study of isolated particles will be essential for searches of new physics, such as the decayH → l+l−l+l−. Colour Figure 2-ii shows the decay H → ZZ* → e+e−e+e− at the design luminosityof 1034 cm-2s-1. To aid in the understanding of these processes, single electrons, muons, andphotons have been used extensively for studies of resolution and to study pattern recognition ina simplified environment. These have been generated directly from within GEANT [2-5].

Ks0

H bb→



2.4.3 Hadronic Decays of Higgs Bosons

Hadronic decays of Higgs bosons have been used extensively as a means of testing pattern rec-ognition within a jet of particles. Further, these decays have led to studies of the b-tagging capa-bility of the ATLAS Inner Detector which can be directly compared with physics requirements.In particular, comparison has been made between the decays and backgroundswhere x is a u-, d-, s-, c-quark or gluon. While these background processes actually have negli-gible rates, the decays are considered representative of actual backgrounds which will be en-countered at the LHC, and by generating them from Higgs decays, direct comparisons can bemade with background jets having the same kinematics as the b-jets. Complete events,p + p → H + W + X with W → μν have been generated with PYTHIA [2-6].

Previous studies [2-7][2-8] concentrated on b-tagging for a light Higgs (mH = 80-100 GeV) sincethis is a plausible method for identifying a Standard Model Higgs in this mass range [2-9]. Inthese studies, the rejection of gluon jets was found to be limited by gluon splitting to heavy fla-vour, and no limitations arising from pattern recognition were observed. Therefore, for this re-port, the emphasis has been put on mH = 400 GeV, which provides a greater test of the two-trackseparation and pattern recognition capability of the Inner Detector. At this mass, the decay tob-jets would have a very small branching ratio. Nevertheless, this decay mode has been used asa ‘factory’ for producing high-pT b-jets. Such jets might be seen in the decays of light SUSYHiggs which in turn may come from the decays of heavy supersymmetric particles[2-10]. Colour Figure 2-iii shows a typical event at low and design luminosity.

2.4.3.1 Properties of H → bb Events with mH = 400 GeV

Figure 2-1 pT distribution of b-jets from ,mH = 400 GeV.

Figure 2-2 |η| distribution of b-jets from ,mH = 400 GeV.

H bb→ H xx→

h bb→

0

50

100

150

0 200 400 600

Jet pT (GeV)

Eve

nts

0

25

50

75

100

0 1 2 3

|η|

Eve

nts

H bb→ H bb→



Figure 2-1 shows the pT distribution of theb-jets (mean is 200 GeV) and Figure 2-2 showsthe |η| distribution (mean 1.1). The chargedmultiplicity of particles with pT >1 GeV, in acone ΔR ≤ 0.4 is shown in Figure 2-3. Thecharged multiplicity in the cone has a mean of10.0, 40% of which comes from daughters ofthe B-hadron decay. In 4% of the jets, there areno charged particles with pT > 1 GeV in thecone.

In a cone ΔR ≤ 0.4, the mean number of pho-tons is 18, of which 9.5 have pT > 1 GeV.

The distance ΔR of charged particles to the b-quark direction in η−φ is shown in Figure 2-4. FormH = 400 GeV, 90% of particles are found in a cone of ΔR ≤ 0.4. The pT distribution of these par-ticles is shown in Figure 2-5. The average pT of particles (pT > 1 GeV) is 10 GeV - 70% of parti-cles have pT less than this. The conclusion is that it is necessary to reconstruct accurately ~4tracks arising from B-hadron decays with pT < 10 GeV in a region where multiple scatteringdominates the impact parameter resolution.

Figure 2-4 Distance ΔR of particles to b-quark direc-tion.

Figure 2-5 pT of tracks in a b-jet, mH = 400 GeV.

Figure 2-3 Charged multiplicity of particles withpT > 1 GeV in ΔR < 0.4 around a b-jet.

0

100

200

300

0 10 20 30

Jet MultiplicityE

vent

s

0

1000

2000

3000

0 0.2 0.4 0.6 0.8 1

ΔR

Tra

cks

0

2000

4000

6000

0 10 20 30 40 50

Track pT (GeV)

Tra

cks



2.4.4 Minimum Bias Events

Minimum bias events account for the vast ma-jority of interactions which will result frombeam collisions in ATLAS; by implication,they do not contain hard-scattering processes.These events are of little interest per se, but atthe high luminosities proposed for the LHC,multiple collisions within one beam-crossingwill be inevitable, causing signal events tohave several minimum bias events superim-posed. The pile-up of these events on top ofsingle particles is essential for realistic studiesof pattern recognition and is discussed inmore detail in Section 2.6.

Minimum bias events have been generated in-dividually using PYTHIA 5.7. The processesof interest for tracking studies are the inelastic,non-diffractive p-p interactions, labelled inPYTHIA as ‘QCD high-pT processes’1. Theη distribution of charged particles in singleminimum bias events is shown in Figure 2-6.Comparison is made with the distributionfrom events containing a hard scatter, namely (mH=400 GeV). The latter is averagedover many events, but is quite different in character due to the high density of particles to befound in the jets.

The pT distributions are shown in Figure 2-7, while the integrals of the pT distributions areshown in Figure 2-8. It can be seen that the average charged particle multiplicity per unit of η,dN/dη, for a single minimum bias event is 7.5 (no pT cut), falling to 0.64 for pT ≥ 1 GeV and0.006 for pT ≥ 5 GeV. The mean dN/dη for neutrals is 9.1, 90% of which are photons, and themean ET is 235 MeV [2-2]. Consequently, the number of charged particles with pT ≥ 1 GeV fromthe pile-up of minimum bias events is 1.2 within a cone ΔR ≤ 0.4 around a b-quark at a luminos-ity of 1034 cm-2s-1.

1. The switches set in PYTHIA are: MSEL=1, MSTP(2)=2, MSTP(33)=3, MSTP(81)=1, MSTP(82)=4.

Figure 2-6 η distribution of charged particles (no pTcut). Dashed line corresponds to all particles in anevent containing the decay of a 400 GeV Higgs tob-jets.

0

5

10

15

20

25

-10 -5 0 5 10

ηdN

/dη

Min Bias

H→bb-

H bb→



2.5 ATLAS Software

The simulation of physics events in the ATLAS detector is performed in a number of steps. Theresults of each step are stored in a set of ZEBRA [2-11] banks.

2.5.1 Overview of Different Software Steps

Physics GenerationFor events other than single particles, four-vectors are generated using PYTHIA and the frag-mentation packages provided by JETSET [2-6]. The complete particle-level information issaved in the event history banks GENZ.

Detector SimulationParticle four-vectors are extrapolated through the ATLAS detector using the GEANT package[2-5]. This extrapolation allows for: the magnetic field provided by the solenoid, ionisation ener-gy loss, multiple scattering, bremsstrahlung, photon conversions, nuclear interactions ofhadrons and the decays of long-lived particles. All stable particles generated by PYTHIA andthose which are created by interactions in the detector are stored in the KINE banks. The energydeposited in sensitive volumes of the detector is recorded in the HITS banks. This relies on hav-ing an accurate geometrical description of the detector, which is provided by the ATLAS inter-face to GEANT, called DICE (Detector Integration CodE). For most of the Inner Detectorsimulation work, the calorimeters have not been included.

DigitisationThe simulation of the electronic response of the detector to particles is also provided by DICE.The response to the HITS is obtained in a form similar to that which might be expected from thereadout electronics after formatting by the online computers. These channel numbers, times, en-ergies, etc. are stored in the DIGI banks. This relies on having an accurate model of the physical

Figure 2-7 pT distribution of charged particles. Figure 2-8 Average multiplicity per unit of η (|η| ≤ 2.5)as a function of pT cut (corresponding to left handedge of bin).

10-3

10-2

10-1

1

10

10 2

0 5 10 15 20

pT (GeV)

dN/d

p T (

GeV

-1)

Min Bias

H→bb-

|η|<2.5

10-3

10-2

10-1

1

10

10 2

0 5 10 15 20

pT cut (GeV)In

tegr

al <

dN/d

η>

Min Bias

H→bb-

|η|<2.5



processes by which signals are collected and transformed by the readout electronics. It is at thisstage that the HITS from several collisions can be combined to produce the effective digitisa-tions which would be observed from the superposition of several events at high luminosity.

ReconstructionThe final stage is to convert the digitisations into physical quantities such as energies, coordi-nate positions, etc. In the Inner Detector, the reconstructed coordinates are used for pattern rec-ognition and subsequently track fitting (described below). The reconstructed quantities arestored in the RECB banks.

AnalysisMany of the studies included in this report are based on the analysis of the RECB banks using aninteractive programming environment called ATLSIM. This program also provides an interfaceto GEANT and permits all of the above simulation steps to be performed, if desired. In particular,it was used to make the pile-up datasets.

Table 2-1 shows the average CPU time in HP9000/735 seconds1 for the different simulationsteps.

2.5.2 Code for Pattern Recognition and Track Fitting

Two pattern recognition programs, iPatRec and xKalman, have been used extensively for thestudies reported in this report. A third program, PixlRec, has been used for certain work.

2.5.2.1 iPatRec

iPatRec initiates track-finding from space-points in the precision tracker. It is designed to ex-ploit the superior two-track resolution and relatively low occupancy of the pixel and SCT track-ing layers.

In its initialisation phase, iPatRec creates a geometry data-base [2-12] describing each moduleof the precision tracker, the layers of the TRT detector and a simplified model of the inert sup-port/service material. In each case, details of the geometry, material thickness and detector res-olution are provided, along with keys to the appropriate hit decoding, clustering andspace-point building algorithms. The track following and fitting routines make extensive use ofthis data-base.

1. Multiply by 27 to obtain CERN unit seconds, and 2.5 to obtain SPECint95 seconds.

Table 2-1 CPU time needed for simulation steps in the Inner Detector. These numbers are representative and,in practice, depend significantly on a number of factors.

GenerationTime (s)

SimulationTime (s)

DigitisationTime (s)

Recon.Time (s)

EventSize (Mb)

Single Track - 2 1 0.1 0.01

1 180 100 20 1

Min. Bias 1 75 - - 0.3

Pile-up at 1034 - - 280 900 10

H bb→



Reconstruction is performed in roads which join the vertex region to a seed region defined onthe outer surface of the Inner Detector. Typical seeds are electron/photon candidates from theEM calorimeter, jets from the hadron calorimeter and tracks found in the external muon detec-tors. For convenience, Inner Detector studies frequently seed from the Monte Carlo information.

Space-points in the road are collated into 4 partitions according to their relative distances fromthe vertex region. By design, the Inner Detector is expected to provide ≥ 6 space-points on atrack. The first and last partitions are defined such that a track from anywhere in the vertex re-gion would have ≥ 2 space-points in the absence of detector inefficiency. Space-point combina-torials from 3 different partitions form track candidates. The first partition is obligatory, whichgenerally ensures a hit in the first two pixel layers. Primary tracks undergoing secondary inter-actions are recovered down to the minimum length providing sufficient hits by performingtrack finding in the first three partitions.

A local helix interpolation between these space-points is used to associate the remaining hitsand to take note of any ‘holes’ (active detector traversed without a hit). This procedure com-bines the precision of interpolation with the ability to follow catastrophic processes such as anelectron bremsstrahlung in the vicinity of the intermediate point. A histogramming technique isused to select the TRT hits to be added to the track [2-13]. This technique also resolves left/rightdrift ambiguities. Tight cuts are made on the straw residual (~2σ) and on the ratio of found toexpected straws, in order to limit high luminosity (and jet core) occupancy effects.

Extra parameters are included in the track fitting to follow multiple Coulomb scattering, and inthe case of an EM calorimeter seed, to allow for electron bremsstrahlung [2-14]. The clusteredhit-pattern in each discrete detector layer is examined in a track-dependent context to allot ei-ther a weight consistent with the expected detector resolution or a reduced weight for possiblybadly-resolved clusters.

Tracks are ranked by quality which is defined according to the radial track length, the absenceof holes and the track fit χ2 (in order of precedence). A search strategy which extracts the high-est quality track candidate from the remaining unused space-points has been devised to pro-vide efficient track finding for a reasonably modest expenditure of computer-time. In particular,the ranking ensures that tracks with TRT confirmation are found first.

Under the default operating conditions1, to be accepted, a track has to fulfil the following re-quirements:

• Number of precision hits ≥ 7.

• Number of ‘holes’ in precision layers upstream of last hit ≤ 3.

• Fit χ2 per degree of freedom < 3.0. This is relaxed to 5.0 for EM calorimeter seeds.

• pT > 1 GeV.

In addition there are some implicit cuts contained in the code:

• Fraction of precision hits shared with other accepted tracks < 50%.

• Number of hits in first partition (approximately the first two pixel layers) ≥ 1.

• Number of space-points on a track ≥ 3, of which ≥ 2 should be unique.

• |d0| ≤ ~2 mm and |z0| ≤ ~20 cm.

1. The cuts can be modified by a user.



2.5.2.2 PixlRec

The pixel detectors provide true space-points of high precision and good two-track resolution,thanks to their high granularity. PixlRec [2-15] is a pattern recognition package designed toexploit these features: track-finding is initiated from the innermost pixel layers and goes out-wards. The package is intended mainly to perform precise tracking in small regions where thetrack density is high, for example inside a jet.

The combinatorial search in the pixel detectors is completed by using the hits in the SCT. Thetrack finding algorithm is flexible, since it uses an abstraction from the actual detectors whichrelies on the hyperplane concept. A hyperplane is a set of different parts from various sub-de-tectors, built according to some symmetry and periodicity rules which are defined in the AT-LAS reconstruction software. Furthermore, this concept has some allowance for treatinginefficiencies in the precision detectors by introducing some redundancy into each hyperplane.Remaining precision hits within a narrow road around the candidate track are associated usingthe Kalman filter algorithm [2-16], the code for which has been developed for the xKalmanpackage (see below). For the final fit, precision is improved using TRT hits with the conformalmapping method developed for xKalman.

2.5.2.3 xKalman

xKalman is a package for global pattern recognition and track fitting for charged particle trackswith pT > 0.5 GeV [2-17]. Pattern recognition is initiated by finding track segments in the TRTand can be performed over a limited region or over the complete Inner Detector. For the recon-struction, xKalman uses two different techniques: a histogramming method and the Kalman fil-ter-smoother formalism [2-16]. The former is suitable for the track finding in the TRT and thelatter for high granularity detectors such as pixels or silicon strips. The framework of xKalmancontains three steps.

The first step of the track finding process is a global pattern recognition in the TRT, which deliv-ers as an end-product a set of possible track candidate trajectories. The global pattern recogni-tion algorithm is applied in the 2-D projections most natural to the geometry of the TRT, i.e. inthe R-φ plane for the barrel TRT and in the z-φ plane for the end-cap. The straight-line track rep-resentation allows the use of the same histogramming method in the different parts of the TRT.The drift-time information from the straws is not used in this first step. Each of these trajectoriesis defined as an initial helix, with its own set of parameters and covariance matrix. This helix isthen used to define a track road through the precision tracker, along which are collected all themeasured hits in each layer.

For the second step, the program attempts to find all possible helix trajectories within the initialroad and with a sufficient number of precision hits. During this step, the tracking and the fittingare performed simultaneously using the Kalman filter-smoother formalism. The essential ingre-dient in the algorithm is the treatment of multiple scattering ‘noise’ contributions and bremsst-rahlung energy losses during the track search procedure.

For all candidate trajectories, xKalman produces first a so-called μ-fit, which only accounts formultiple scattering and ionisation energy losses. If the track candidate was identified as an elec-tron in the TRT (or flagged as such by the user), xKalman produces a so-called e-fit1, which ac-

1. Commonly referred to as the brem-fit - but quite distinct from the fit including the EM calorimeter inSection 6.1.



counts for bremsstrahlung energy losses in addition1. The result of the e-fit is only used byxKalman for the final track output, if the fit increases the number of accepted measurementpoints from the precision layers with respect to the μ-fit.

Each candidate helix trajectory is assigned a quality, calculated on the basis of the total numberof hits in the precision layers. A cut is applied at the end of this second step to reject the ambig-uous trajectories of insufficient quality.

In a third step, the accepted helix trajectories are then extrapolated back into the TRT, where anarrow road can be defined around the extrapolation. Obviously, the width of this road is deter-mined by the errors on the helix trajectory. All straw hits with their drift-time information with-in this road are then included for the final track finding and track fitting steps.

Under the default operating conditions2, to be accepted, a track has to fulfil the following re-quirements:


• Number of precision hits not shared with another track ≥ 6.

• pT > 0.5 GeV.

• Number of TRT hits ≥ 9.

• Fraction of straws hit out of number crossed ≥ 0.70.3

2.6 Pile-up at High Luminosity

The cross-section for inelastic, non-diffractive pp interactions at LHC energies is expected to be70 mb. At a design luminosity of 1034 cm-2s-1 and with a bunch spacing of 25 ns, the meannumber of minimum bias events which should be seen by the Inner Detector is 18. However,since approximately 20% of the bunches in the LHC will be empty, the average time betweenfilled bunches is increased and the mean number of collisions is about 23 for these non-emptybunches. This implies that when an interesting event is selected by the trigger, on average, therewill be 23 single minimum bias events superimposed - these events are referred to as pile-up.The effect of pile-up can be seen in Colour Figure 2-iii.

The bunch structure in LHC is such that there will be many successive filled bunches followedby successive empty bunches. This means that an interesting event will usually follow and befollowed by beam-crossings containing pile-up events. Consequently there is the potential forcollisions from previous and following beam-crossings to be seen by the detector - this dependscritically on the response of the individual sub-detectors. In particular, low-pT tracks(pT < 500 MeV) from bunch-crossings prior to the event of interest will spiral in the solenoidalmagnetic field for extended periods of time (up to 100 ns) and may be seen. Such tracks are re-ferred to as loopers.

1. Bremsstrahlung is handled in a similar way to multiple-scattering. At each layer, the program makes acorrection to the track curvature to allow for the bremsstrahlung and adds a ’noise’ term to the covari-ance matrix.

2. The cuts can be modified by a user.3. If there are ≥ 9 precision hits, the track is retained without applying cuts on the TRT information.



Since the silicon strips of the SCT and the silicon pixels have a fast response to charged particles,the signals can be tagged easily so as to be associated to the correct beam-crossing and there islittle contamination by fast particles from out-of-time events. Nevertheless, the detectors arestill sensitive to loopers from previous events, which cause spurious hits.

In the TRT, the maximum drift-time is around 40 ns, which is significantly more than the 25 nsbunch spacing, and the requirement to be as efficient as possible for in-time hits necessitates agate which accepts some hits from fast particles from out-of-time events as well as hits fromloopers.

With the exception of the TRT drift-time information, the default GEANT simulations of the AT-LAS Inner Detector do not allow for event timing, particle propagation or signal propagation(the speed of light is effectively infinite). Loopers are allowed to propagate for a distance corre-sponding to 100 ns, although they tend to be lost from the detector because they exit the InnerDetector and hit the end-cap calorimeter or they lose energy due to interactions.

Pile-up is simulated by superimposing on top of the GEANT HITS from signal events those fromN minimum bias events which have been selected quasi-randomly from a pool of such events,with N distributed according to Poisson statistics. With this procedure, no account is taken ofthe collision time of the interaction which produced the hits, instead all N events are treated asin-time. For the silicon detectors, N should be 231. However, for the TRT, to allow for the extrahits which are expected, N is chosen as 32. In reality one would expect to see a fraction F of thehits from all tracks from out-of-time events. When reconstructed with the assumption that theywere in time, these hits would be staggered about the true track positions to the left and rightdepending on the drift direction in the straws. Instead, the standard simulation superimposesall the tracks in the TRT from a number of additional minimum bias events - this number is thefraction F of the number of events in a single beam-crossing. These TRT hits are added in-time,hence they are explicitly correlated (i.e. they will really look like tracks in the TRT). It is the be-lief that this creates a more difficult environment for pattern recognition than would be seen inreality.

To understand precisely these issues, a more complete simulation has been performed for theTRT which does describe correctly the time-structure of beam-crossings, particle and electricalpropagation times, and allows particles to loop in the detector for as long as 250 ns. The resultsof these detailed simulations are described in Section 3.7. It is from such studies that the effec-tive number of events to superimpose in the TRT was determined.

For the cases where both the Inner Detector and the calorimeters were simulated at high lumi-nosity, N = 48 minimum bias events were added to the calorimeter information [2-2].

2.7 References

2-1 ATLAS Collaboration, Inner Detector Technical Design Report, CERN/LHCC 97-17.

2-2 ATLAS Collaboration, Calorimeter Performance Technical Design Report, CERN/LHCC96-40.

2-3 D. Froidevaux and A. Parker, ATLAS Internal Note, INDET-NO-046.

1. Actually use 24 for technical reasons.



2-4 Particle Data Group, Phys. Rev. D54 (1996).

2-5 R. Brun et al., GEANT3, CERN DD/EE/84-1 (1986).

2-6 T. Sjostrand, Computer Physics Commun. 82 (1994) 74.

2-7 I. Gavrilenko et al., ATLAS Internal Note, INDET-NO-115.

2-8 S. Haywood, ATLAS Internal Note, INDET-NO-116.

2-9 D. Froidevaux and E. Richter-Was, Z. Phys. C67 (1995) 213.

2-10 LHCC Workshop on SUSY.

2-11 CERN Program Library, Q100.

2-12 R. Clifft and A. Poppleton, ATLAS Internal Note, SOFT-NO-009.

2-13 J. Loken and A. Reichold, ATLAS Internal Note, INDET-NO-132.

2-14 A. Clark et al., ATLAS Internal Note, INDET-NO-015.

2-15 L. Vacavant, Ph.D. Thesis, University of Marseille (in preparation, for May 1997).

2-16 P. Billoir, Nucl. Instrum. Methods 225 (1984) 352.

2-17 I. Gavrilenko, ATLAS Internal Note, INDET-NO-165.


3 Simulation 43

3 Colour Figures

Figure 3-i Longitudinal view of the ATLAS Inner Detector.

TR

T

Pixe

lsSC

T

Bar

rel

patc

h pa

nels

End

-cap

patc

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ices

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44 3 Simulation

Figure 3-ii Longitudinal view of half of the ATLAS Inner Detector.


3 Simulation 45

Figure 3-iii Transverse view of ATLAS Inner Detector. The TRT is shown in a simplified form: each blue circlerepresents approximately a layer of straws.

TRT

Pixels SCT


46 3 Simulation

Figure 3-iv Transverse view of a quadrant of the ATLAS Inner Detector (precision layers only). From the centre(lower left-hand corner) are: a) the beam pipe, b) three layers of the barrel pixel tracker: ladder support structure(green), silicon crystal (black) with the active regions (red) and support cylinders (dark blue), c) the overall cylin-drical stiffener of the barrel pixel detector (dark blue), d) four layers of the SCT tracker: support (green), lumpedpower cables and cooling (red circles), active silicon (pink) and electronics boards (pale blue), and e) the SCT’sinsulating layer (black).


3 Simulation 47

3 Simulation

3.1 Layout

This section describes the layout of the ATLAS Inner Detector in the simulations which havebeen used for the bulk of the work presented in this document. The layout used for simulationwas frozen in September 1996. Subsequently there have been some changes of the design whichis presented in the second volume of this TDR. Significant differences between the final designand that used for the simulation are summarised in Section 3.1.5.

The following paragraphs will describe in detail the layouts of the three main components ofthe Inner Detector: the pixel detector, the silicon-strip detector (SCT) and the transition radia-tion tracker (TRT). This is followed by a short section describing the simulation of the serviceswhich pass between the detectors. Longitudinal (R-z) and transverse (x-y) projections of thecomplete detector, along with expanded views, are shown in Colour Figures 3-i to 3-iv. In thesefigures, the TRT is shown in a simplified form; a more detailed figure can be found inSection 3.1.3.

3.1.1 Pixel Detector

The pixel detector consists of a barrel tracker and two symmetric end-cap trackers. A 3-D viewof the whole simulated pixel detector can be seen in Figure 3-1.

3.1.1.1 Pixel Barrel

The barrel pixel tracker is made of barrel pixel modules arranged in three cylindrical layers. Theinnermost layer will be referred to here as the B-layer (or layer 0), followed by layers 1 and 2 atincreasing radii. The individual layer radii, their active half-lengths, tilt angles, and the numberof modules per layer are given in Table 3-1.

A barrel pixel module is represented as two plates. The first plate, which represents the siliconcrystal, is 6.58 cm long (in the z-direction), 2.54 cm wide and 150 μm thick. The second plate,which represents the electronics chip bonded to the crystal, is 6.18 cm long, 2.04 cm wide and130 μm thick. The electronics plate is positioned on the inner side of the silicon crystal. The cen-tre of the crystal detector plate is shifted by 0.05 cm with respect to the centre of the electronicschip plate in order to have a 0.3 cm wide space for busing and small driver chips on one side ofthe module. On the other three sides, the guard area is 0.2 cm wide. The pixels themselves, sim-ulated at the digitisation phase, are 50 μm wide (in Rφ) and 300 μm long (in z).

These barrel modules are arranged end-to-end on long ‘ladders’ which lie parallel to the z-axisof the detector. The ladders of the B-layer consist of 13 modules attached to a service ladder (de-scribed below). Overlap of the active area in the z-direction is achieved by having alternatemodules shifted 0.03 cm above and 0.03 cm below the nominal radial position; seven modulesare at the larger radius and six are at the smaller radius. The positions of the modules in thez-direction are chosen to obtain a uniform projected overlap for particles coming from within 2σin |z| of the nominal interaction point at z = 0. Layer 1 also has 13 modules per ladder, buttheir z positions are different compared to the B-layer in order to optimise the projective z-over-


48 3 Simulation

lap. The 11 modules per ladder in layer 2 also are arranged with minimum z-overlaps to insurehermeticity.

As can be seen in Colour Figure 3-iv, the pixel ladders are tilted in φ as they are arranged aroundeach barrel layer. This tilt performs two functions: it provides overlap in the φ-direction of theactive area of the modules, and it allows the charge division between neighbouring pixels to-gether with the Lorentz effect to be used to increase cluster widths, with the aim of improving

Figure 3-1 Pixel detector in 3-D.

Table 3-1 Parameters of barrel pixel layers.

Layer R (cm)

Active half- length (cm)

Number ofmodules in z

Number ofladders in R-φ

Tilt angle (degrees)

B-layer 4.0 38.4 13 16 + 10.5

Layer 1 11.0 38.4 13 44 + 9.5

Layer 2 14.2 33.8 11 58 + 9.5


3 Simulation 49

the Rφ resolution. The design provides hermeticity for pT ≥ 0.5 GeV for a vertex position±11.2 cm. This results in an Rφ overlap of 5 pixels in the B-layer.

Each barrel service ladder includes mechanical support elements, cooling tubes with heat con-ductors and electrical cables. This service structure is represented in the simulation by a platewith a half-length of 42.5 cm in the z-direction and width of 1.6 cm. For layers 1 and 2, the cool-ing tubes were assumed to be made of aluminium with a thickness of this plate of 0.73% X0; forthe B-layer it is assumed that the cooling tubes are made of beryllium instead of aluminium, re-ducing the total service ladder thickness to 0.60% X0.

3.1.1.2 Pixel End-caps

Each end-cap pixel tracker is made of end-cap pixel modules arranged in rings, which are inturn arranged on disks.

An end-cap pixel module is represented as two trapezoids. This is shown in Figure 3-2. The firsttrapezoid, which represents the silicon crystal, is 5.3 cm high; its inner edge is 1.249 cm long, itsouter edge is 1.491 cm long, and it is 150 μm thick. The active area of this silicon crystal is a trap-ezoid with height 4.94 cm, inner edge 0.72 cm and outer edge 0.96 cm. The second trapezoid,which represents the electronics chip bonded to the crystal, is 4.94 cm high; its inner edge is 1.02cm long, its outer edge is 1.26 cm long, and it is 130 μm thick. The side of the electronics chip isshifted by 0.2 cm with respect to the crystal. As in the barrel, the pixel sizes are 50 μm by300 μm.

These end-cap modules are arranged in rings. Modules which are adjacent in φ are mounted onalternate sides of a support and cooling ring. The arrangement of the modules alone is shown

Figure 3-2 Pixel end-cap module. The ‘inner face’refers to the face which is towards the support disk.

Figure 3-3 Pixel end-cap ring. The support disk is notshown but is located between the two partial rings.The electronics boards are indicated by dashed lineson the outer faces; the active silicon by shadedregions on the inner faces.

siliconcrystal active

regionelectronics

board

outerface

innerface


50 3 Simulation

Figure 3-3. The modules are positioned to give an active overlap in Rφ of 200 μm. There are twotypes of rings: inner and outer and their parameters are given in Table 3-2.

In turn, the rings are arranged on four disks, which are numbered from 1 to 4 with increasing|z|. The z-positions and minimum and maximum radii of the active areas of the disks are givenin Table 3-3.

3.1.1.3 Pixel Material

Tables 3-4 and 3-5 show breakdowns of the material used in the simulation for one layer of thebarrel and end-cap pixel tracker, respectively. Not all of the corresponding services, which havebeen simulated, are contained in the tables.

a. Consists of mechanical structure, cooling tube, coolant and cables, which are simulated as carbon, alu-minium, water and aluminium respectively.

Table 3-2 Parameters of pixel end-cap rings.

Ring type Number ofmodules

Active Rmin(cm)

Active Rmax(cm)

Support + coolingring thickness

(cm)

Inner 108 11.00 15.94 0.42

Outer 144 15.90 20.84 0.30

Table 3-3 Parameters of pixel end-cap wheels.

Wheel number z position (cm)

Ring type(s) Active Rmin(cm)

Active Rmax(cm)

1 47.3 inner,outer 11.00 20.84

2 63.5 inner,outer 11.00 20.84

3 77.6 inner,outer 11.00 20.84

4 107.2 outer 15.90 20.84

Table 3-4 Pixel barrel material.

Item Material Size Radiation Length (%)

no overlap with overlap

Wafer of pixels Silicon 6.58 × 2.54 cm2 ×150 μm

0.16 0.28

Electronics chips Silicon 6.18 × 2.04 cm2 ×130 μm

0.14 0.19

Laddera 42.5 × 1.6 cm2 0.73 0.74

Support structure Beryllium 0.11

Outboard cylinder Beryllium 0.07

Total 1.39


3 Simulation 51

3.1.2 SCT

The SCT, like the pixel detector, consists of a barrel detector and two symmetric end-cap detec-tors.

3.1.2.1 SCT Barrel

The barrel SCT is made of barrel SCT modules arranged in four cylindrical layers. The parame-ters of the different barrel layers are given in Table 3-6.

To form a barrel SCT module, two rectangles are joined together at their long sides. The first rec-tangle, which is simulated as silicon, represents two 6.36 × 6.36 cm2 silicon crystals bonded to-gether edge-to-edge. It is 12.82 cm long and 300 μm thick. At the digitisation phase of eventsimulation, a dead region of 1 mm is simulated all around the perimeter of each square crystalto simulate the guard ring, which leaves 6.16 cm of active silicon across the width of the detec-tor, corresponding to 768 strips of 80 μm. On each end of the module, an additional 0.5 mm ofdead space is simulated, to represent the space occupied by the resistor chain. This leaves an ac-tive length of 12.52 cm, with a dead space of 2.2 mm (twice the width of the guard ring plus0.2 mm for bonding) running across the width at the centre of the module.

The second rectangle, which is simulated as copper, represents the electronics board. It is2.14 cm wide, 11.0 cm long and 0.6% of a radiation length thick. The electronics board and thecrystal are joined together at their long edges.

a. Consists of mechanical structure, fibre interior, cooling tube, coolant and cables, which are simulated ascarbon, carbon, water and aluminium respectively

Table 3-5 Pixel end-cap material.

Item Material size Radiation Length (%)


Wafer of pixels Silicon 5.0 × 1.491 cm2 ×150 μm

0.16 0.27

Electronics chips Silicon 6.18 × 2.04 cm2 ×130 μm

0.14 0.23

Inner (outer) diska ΔR = 4.87 (4.97) cm 0.40 (0.46) 0.40 (0.46)

Total inner (outer)disk

0.90 (0.96)

Table 3-6 Parameters of SCT barrel.

Layer R(cm)

Active half- length (cm)

Number ofmodules in z

Number ofstaves in φ

Tilt angle (degrees)

1 30.0 74.5 12 32 10.0

2 37.3 74.5 12 40 10.0

3 44.7 74.5 12 48 10.0

4 52.0 74.5 12 56 10.0


52 3 Simulation

Two of these double rectangles are then sandwiched together, 0.1 mm apart, to form a barrelSCT module. The innermost rectangle is given a relative rotation (stereo angle) of 40 mrad withrespect to the outermost, which lies with its long axis parallel to the beam-pipe. This stereo rota-tion has opposite sign for alternate barrel layers.

The barrel modules are arranged end-to-end on long staves which are installed to lie parallel tothe z-axis of the detector. Each stave (represented by a rod of carbon 1 cm wide, 149.8 cm longand 1% of a radiation length thick) holds 12 modules; alternate modules are staggered ±1 mmabove and below the nominal layer radius to allow overlap of the active area in the z-direction.The positions of the modules in the z-direction are chosen to obtain projective overlap of the ac-tive regions of the modules for all tracks coming from within 2σ in |z| of the nominal interac-tion point at z = 0.

As can be seen in Colour Figure 3-iv, the SCT staves are tilted in φ as they are arranged aroundeach barrel layer. This tilt provides overlap in the Rφ direction of the active area of the modules(typical overlap is 1-2 mm), and it allows the Lorentz effect to be used to minimise clusterwidths, thereby improving two-track separation capabilities. There is an eight-fold symmetry inthe complete SCT barrel. By aligning the centres of the modules at φ = 0, the denser material ofthe services and supports does not point radially, minimising the inhomogeneities in the azi-muthal distribution of the material.

The staves are represented as being mounted on carbon cylinders 0.3% of a radiation lengththick and 147.8 cm long. An interlink wheel and a flange are represented at either end of eachcylinder. The interlink wheel is 1 cm long in the z-direction and 1.5% of a radiation length thickin the radial direction; the flange is 1.2% of a radiation length thick in the z-direction and 3 cmlong in the radial direction for layers 1 and 2, and 4 cm long for layers 3 and 4. Running along-side the staves are copper pipes, increasing in diameter from 0.13 cm at z = 0 to 0.16 cm at theextreme ends of the staves, to represent cooling pipes and power cables. Surrounding the wholebarrel detector is an insulating layer of 0.45% X0.

3.1.2.2 SCT End-caps

Each end-cap SCT tracker is made of end-cap SCT modules arranged in rings, which are in turnarranged on wheels, similarly to the pixel end-cap detector arrangement. In the simulation, themodules at inner radii are made of gallium arsenide, the modules at outer radii are made of sil-icon.

To form one layer of a end-cap SCT module, a trapezoid of active semiconductor (silicon or gal-lium arsenide), representing two smaller trapezoids bonded together, is attached to a rectangu-lar piece of silicon representing the electronics board. The actual material used to simulate thiselectronics board is silicon with twice the normal density to account for the presence of fan-ins,glue, printed films, etc. The electronics board is 3 cm high, 320 μm thick, and the same width asthe shorter base of the sensitive trapezoid. The exact size and shape of the sensitive trapezoiddepends upon what radial position it will occupy in ATLAS: for example a module destined forthe outermost possible radial position is 12.4 cm high, and the inner and outer edge lengths ofthe trapezoid are such that when it is placed in its final position, it covers a uniform 7.38° in φ.As in the barrel module, at digitisation time, a dead area is left all around each of the two small-er trapezoids, and each trapezoid is divided into 768 strips. These strips are keystone-shaped,that is, their width is uniform in φ when they are placed in their final position in ATLAS. Be-cause the width of the modules depends upon which wheel they will be mounted, the strip


3 Simulation 53

pitch does too. It is about 63 μm at the centre of a GaAs module and on average about 85 μm atthe centre of a silicon module.

To form an end-cap SCT module, two of these trapezoid-rectangle combinations are attached toa 300 μm thick beryllia substrate, with one being attached on one side so that its strips will beradial and the other on the other side with a 40 mrad rotation (stereo angle). This stereo rotationhas opposite signs for adjacent wheels. The module is mounted on an aluminium block, repre-senting support and cooling, which is 0.55 cm thick, 1.2° wide in φ, and 1 or 2 cm high (1 cm forthe inner ring, 2 cm for the outer ring).

Figure 3-4 shows an end-cap SCT module and illustrates how these modules are arranged inrings. On the ring, modules which are adjacent in φ are separated by 0.25 cm in z to allow activeoverlap in the φ-direction; this overlap is on average about 1 mm wide. There are four types ofrings, each of which is intended to cover a different radial range. Table 3-7 gives the parametersof the different SCT rings.

The rings are in turn arranged on nine wheels, which are numbered from 1 to 9 with increasing|z|. As can be seen in Figure 3-5, rings which are adjacent in R are positioned on alternate sidesof the wheel support disks (described below) to provide projective overlap of the active regions

Table 3-7 Parameters of SCT rings.

Ring type Material Number ofmodules

Active Rmin(cm)

Active Rmax(cm)

1 Silicon 52 43.8 56.0

2 Silicon 40 33.4 45.1

3 Silicon 40 39.9 45.1

4 GaAs 40 26.0 33.1

Figure 3-4 End-cap SCT module, with part of a ring.The electronics boards are shaded.

Figure 3-5 Cross-section of SCT wheel. For clarity,only the modules and support disk are shown.

activesilicon

electronics

GaAs

electronics

activesilicon

electronics

support disk


54 3 Simulation

in the radial direction. This projective overlap is on average about 1 mm wide for tracks comingfrom within 2σ of the nominal interaction point. To avoid line-up in φ of excess material due tothe φ-overlap of adjacent modules on the rings, the wheels are rotated slightly in φ with respectto each other. The |z| positions, minimum and maximum radii of the active areas of thewheels, and relative φ rotations of the wheels are given in Table 3-8.

The support disks themselves are simulated as 1 cm thick annular disks made of ‘carbon fibre’,defined as carbon with density 0.13 g/cm3 and radiation length 328 cm. The solid portion of thedisks cover a radial range from 25 cm to 56.5 cm, where they connect with a 1 cm thick outersupport frame made of the same material. Embedded in the support disks at the point wherethe rings are attached are cooling pipes, simulated as a mixture of aluminium and water withdensity 1.52 g/cm3, to represent aluminium pipes filled with binary ice. These cooling pipesalso run from the vicinity of each wheel, along the outside of the support frame, and then upthrough a crack in the transition radiation tracker. Power cables for the end-cap SCT are repre-sented as aluminium pipes, leading radially outward from the vicinity of the electronics boardsto the support frame, with a crude 1/R spreading effect included. From that point in z they con-tinue running along the support frame and on through the exit crack through the TRT. Sur-rounding the whole end-cap detector is an insulating layer 0.45% of a radiation length thick.

Table 3-8 Parameters of SCT wheels.

Wheelnumber

z position(cm)

Ringtype(s)

Active Rmin(cm)

Active Rmax(cm)

Rotation in φ(degrees)

1 83.5 1, 2, 4 26.0 56.0 0

2 92.5 1, 2 33.4 56.0 2.3

3 107.2 1, 2, 4 26.0 56.0 -2.3

4 126.0 1, 2, 4 26.0 56.0 0

5 146.0 1, 2, 4 26.0 56.0 2.3

6 169.5 1, 2, 4 26.0 56.0 -2.3

7 213.5 1, 2 33.4 56.0 0

8 252.8 1, 3 39.9 56.0 2.3

9 277.8 1 43.8 56.0 -2.3


3 Simulation 55

3.1.2.3 SCT Material

Table 3-9 shows the breakdown of the material in the simulation of one layer of the barrel SCT.In this table, the amount of material in a module’s electronics board (hybrid) has been calculat-ed as if it were smeared uniformly over the area of that module’s silicon wafer. All other materi-al for the layer (support, services) has been smeared uniformly in φ. The effect of overlaps is toincrease the average material seen above that for a single module. The distinction is displayedin the columns no overlap and with overlap of the table.

Table 3-10 shows the breakdown of the material in the simulation of the rings in the end-capSCT tracker. Again the amount of material in a module’s hybrid has been calculated as if it weresmeared uniformly over the area of that module’s silicon wafer. However it should be kept inmind that when a track crosses one of these rings mounted on a wheel, the actual amount ofmaterial it traverses can be quite different from what is quoted in this table because the electron-ics board for a module does not ‘shadow’ that module’s active silicon, but rather that of themodules in a neighbouring ring. Similarly the power cables for the modules on the inner ringsshadow not their own sensitive semiconductor but that of all modules at larger radii. In the ta-ble, the amount of material due to these power cables is treated as though it shadows its ownmodule’s semiconductor. Table 3-11 shows the average amount of material in the simulation ofsingle SCT wheels. The total amount of material in the wheel has been smeared over the entirearea of that wheel. This calculation includes the effects of R and φ overlaps of modules. Both ofthe above tables show what the effect would be on the material budget in the simulation if the200 μm thick GaAs wafers in ring 4 were replaced with 300 μm thick silicon wafers of the samesize and shape.

a. Allows for hybrid, chips, fan-ins, glue, printing, washers and connectors.

Table 3-9 SCT barrel material.

Item Material Size Radiation Length (%)


Detectors (wafers) Silicon 6.36 × 12.82 cm2 ×600 μm

0.64 0.70

Hybrida Copper 2.14 × 11.0 cm2 ×0.6% X0

0.35 0.38

Mounting Block Carbon 1 cm wide ×0.19 cm thick

0.17

Support cylinder Carbon 0.30

Services (cooling,cables)

Copper 0.128 cm thick atη=0

0.61 at η=0(0.950 at end)

Total 2.16 at η=0


56 3 Simulation

a. Contributions to ring 4 correspond to GaAs; effects of using silicon instead are indicated in brackets.b. Allows for hybrid, chips, fan-ins, glue, printing, washers and connectors.c. Allows for mounting block, insert and fasteners.d. Allows for on-wheel pipes and on-wheel cooling.

a. Contributions to ring 4 correspond to GaAs; effects of using silicon instead are indicated in brackets.

Table 3-10 SCT wheel material by rings. Ring 3 is not included, but looks similar to ring 4 when GaAs isreplaced by silicon.

Item Material Ring 1 Ring 2 Ring 4

Size Rad Len(%)

Size Rad Len(%)

Size Rad Lena

(%)

Detectors(wafers)

Si/GaAs 79.7 cm2 ×600 μm

0.64 78.3 cm2 ×600 μm

0.64 36.5 cm2 ×400 μm

1.74 (0.64)

Spine BeO 61.6 cm2 ×300 μm

0.16 59.6 cm2 ×300 μm

0.16 41.2 cm2 ×300 μm

0.23

Hybridb Silicon 16.9 cm2 ×0.13 cm

0.29 22.7 cm2 ×0.13 cm

0.40 16.9 cm2 ×0.13 cm

0.63

Mountingc Alumin-ium

10.2 cm2 ×0.13 cm

0.19 14.7 cm2 ×0.09 cm

0.19 6.5 cm2 ×0.12 cm

0.24

SupportDisk

CarbonFibre

0.30 0.30 0.30

Coolingd Al+ H2O 0.04 0.06 0.10

Powercables

Alumin-ium

0.12 0.09 0.10

Total 1.74 1.84 3.34 (2.24)

Table 3-11 Average material in SCT wheels.

Wheels 1,3-6 Wheels 2,7 Wheel 8 Wheel 9

Rings 1, 2 and 4 1 and 2 1 and 3 1

Inner disk radius 26.0 cm 32.0 cm 38.0 cm 41.0 cm

Outer disk radius 56.5 cm 56.5 cm 56.5 cm 56.5 cm

Item Contributions to Average Radiation Lengtha (%)

Detectors (wafers) 0.91 (0.71) 0.68 0.66 0.56

Spines 0.19 0.17 0.17 0.14

Hybrids 0.43 0.36 0.45 0.26

Mounting 0.22 0.20 0.20 0.16

Support Disk 0.30 0.30 0.30 0.30

On-disk cooling 0.07 0.06 0.07 0.04

Power cables 0.20 0.13 0.16 0.12

Total 2.32 (2.12) 1.90 2.01 1.58


3 Simulation 57

3.1.3 TRT

The TRT consists of a central section which has a barrel geometry for |η| ≤ ~0.5 and twoend-cap sections consisting of multi-plane wheels at higher |η|.

In the simulation, the barrel TRT has a total of 73 layers. Each straw is broken into two electri-cally isolated halves at z = 0, with each half of the straw being read out separately. Each half ofthe barrel TRT is 74 cm long giving the barrel a total length of 148 cm. The barrel region extendsfrom an inner radius of 56 cm to an outer radius of 107 cm. The simulation contains two types ofbarrel layers: short layers which are only active for 40 cm < |z| < 74 cm at smaller radii(R < 63 cm) and full length straws at larger radii. There are also two types of wheels in theend-cap region: short ones where the straws are radially oriented between radii of 64 cm and103 cm and longer ones which have an inner radius of 48 cm and the same outer radius of103 cm, to provide coverage of the full pseudorapidity range. Both the barrel and the wheels usestraws with identical properties (except for the length of the straw). These parameters are sum-marised in Table 3-12.

3.1.3.1 TRT Barrel

The barrel region is simulated inside a tube which encloses the entire barrel detector volume(long- and short-straw barrels).

To model the long-straw barrel layers, the tube is split in halves at z = 0, then into layers in Rand finally in φ into small sections of radiator which enclose one straw and are positioned paral-lel to the beam axis. A single straw (the simulation of which is described later in this section) isthen positioned in each φ-segment. The straw layers are separated by 6.8 mm in R and within alayer the straws are also separated in Rφ by 6.8 mm. The individual straw layers are staggeredby a fraction of a φ-segment so that a stiff track will pass through 32 long straws on average. Thealgorithm used to calculate the stagger gives a unique φ shift to each layer. Figure 3-7 shows adetailed view of the straws in part of the TRT barrel.

The transition radiation material (or radiator) surrounding the straws is modelled as a low den-sity foam and fills the entire volume between the straws (except for a tiny gap around thestraw). Volumes representing the support structure at the inner and outer radii of the barrel areintroduced with the inner support being 1.0% of a radiation length thick in R and the outer sup-port being 1.5% of a radiation length thick in R. The material of the support is taken to be carbonwith its density appropriately adjusted to give the desired radiation length. The small dead area

a. Active length starts at |z| = 40 cm - see text.

Table 3-12 Main parameters of TRT.

Straw type Rmin (cm) Rmax (cm) |z|min (cm) |z|max (cm) Num layers

Barrel

Short 56 62 0a 74 9

Long 62 107 0 74 64

End-cap

Short 64 103 83 278 160

Long 48 103 282 335 64


58 3 Simulation

and electrically insulating material at z = 0 is modelled as a 5 mm long plastic plug in the end ofeach straw. Since the straws butt at z = 0, this provides a total length of 10 mm of dead region.The material of the electronics and support structure on the outer end of barrel is modelled as atube of carbon extending from an inner radius of 55 cm to an outer radius of 108 cm, and havinga thickness in the z-direction of 7% of a radiation length.

The shorter barrel straw tubes (those at R < 62 cm) are modelled identically to the long straws.During digitisation, the hits from the inner dead region (|z| < 40 cm) are ignored. This is inagreement with the current design - having only part of the wire active greatly reduces thecounting rate for these low radii straws. The goal of these short straws is to maintain the largestpossible number of hits recorded on a track in the region around |η| = 1.0, where tracks passthrough both the barrel and end-cap TRT.

This barrel TRT geometry is a simplified approximation to the current design. The simulatedbarrel contains 64 full length layers which is the same as the actual design. There are three lay-ers of modules which causes two straw layers to be lost (one at a radius of about 70 cm and oneat radius of about 86 cm). To simulate these lost layers the simulation takes advantage of the factthat the 51 cm radial extent of the barrel divided by a 0.68 cm layer thickness gives space for75 layers and only 73 are actually required in the barrel. Therefore, at two of the layer positions(numbers 21 and 45) the usual straw/foam layers are replaced with inactive layers of carbonwhich provides an appropriate amount of material to represent the module top/bottom bound-aries including the water filled cooling tubes located in two of the corners of each module. Anadditional effect is that each layer of straws will lose about 32 straws because the sides of barrelmodules are not modelled in the simulation. The net effect of this is that the simulation has anexcess of about 4% barrel straws. The straws in each layer are evenly spaced in φ with each fourconsecutive layers radially having the same number of straws. This is also an approximation tothe real situation where the straws in a module are arranged in flat layers within a module andnot on circular arcs around the beam axis.

Figure 3-6 Transverse view of a quarter section of theInner Detector, where the TRT straw layers areapproximated by arcs of circles.

Figure 3-7 Detailed view of straws in TRT. View cor-responds to box drawn in Figure 3-6.


3 Simulation 59

3.1.3.2 TRT End-caps

Each end-cap is made up of 14 short wheels and 4 long wheels, each containing several planesof radial straws. Each wheel is divided in the z-direction into layers, and then in φ into sectionsof radiator containing one straw, each perpendicular to the beam axis. The active length of ashort straw is 39 cm and the straws are positioned between an inner radius of 64 cm and an out-er radius of 103 cm. Figure 3-8 shows a 3-D cross-section through part of a a TRT wheel, show-ing the radial arrangement of the individual straws. The first wheel has its front face at|z| = 83 cm and the last wheel ends at |z| = 277 cm.

All of the shorter wheels are 12.8 cm thick in the z-direction: the first six have 16 straw planes inz, while the last eight have 8 planes. With the exception of one small gap between the fourthand fifth wheels to allow space for the end-cap silicon strip detector services, the short wheelsare evenly spaced in z and fill the available volume. As in the barrel case the straw layers arestaggered in φ to guarantee a minimum number of hits on a track. A total of eight different val-ues of φ stagger are used; for the wheels with 16 layers, the staggers occur in a different orderfor the first eight and second eight planes. Owing to the radial alignment of the straws, eachstraw increases in its separation from its nearest neighbours with increasing radius and trackspass through more straws at lower radii than they do at higher radii. All short straw layers con-tain 768 straws.

The material used to represent the radiator in the wheels is similar to the material used in thebarrel except for having a slightly different density (0.059 g/cm3 for the 16-plane wheels and0.030 g/cm3 for the 8-plane wheels). Volumes representing the extra material at the inner andouter radii are included in the simulation. The inner support is 1.5% X0 and the outer support is5% X0. As in the barrel case, the material of the supports is taken to be carbon with its densityappropriately adjusted to give the desired radiation length.

The four longer wheels are modelled identically to the short wheels with 16 straw planes exceptfor their length and number of straws. The inner radius of each long disk is 48.0 cm and thelength of the straws is 55 cm. Owing to the smaller inner radius, there are necessarily fewer longstraws (576). The four long straw wheels are positioned evenly between |z| = 282 cm and|z| = 335 cm.

3.1.3.3 TRT Straws

Each straw tube in the detector (there are approximately 372,000 straws) is modelled individu-ally as a GEANT tube containing drift gas and a wire. The straw tube is surrounded by a 50 μmlayer of CO2 for mechanical clearance between the straw and the radiator. The straw itself is85 μm of Kapton (C5H4O2 with a density of 1.39 g/cm3) and has an internal diameter of 0.4 cm.The straw wall is thicker than the actual straw wall to allow for the mass associated with thefour carbon fibres that are glued to the outside of each straw to ensure straightness and tostrengthen the straw. The straw is filled with a mixture of 70% Xe, 20% CF4, and 10% CO2 at at-mospheric pressure. Each straw is simulated with a central copper wire with a radius of 25 μm,which is positioned along the longitudinal axis of the straw.


60 3 Simulation

3.1.3.4 TRT Material

Table 3-13 shows the breakdown of the material in the barrel and end-cap TRT. Since this mate-rial is spread unevenly throughout the TRT, it is not very helpful to consider the averages for in-dividual units. This is especially so for the wheels, where there is a concentration of material atthe outer radius. Instead the breakdown is given as a function of |η|, showing the contribu-tions of the different components.

Figure 3-8 Part of a TRT wheel (complete wheels can be seen in Colour Figure 1-i). The outer surfaces (nearvertical and top) have been shaved away to reveal the radial straws. The material representing the outer sup-ports and electronics is visible at the outer radius. In the GEANT simulation, the disk boundaries really are circu-lar; however when drawn in 3-D, they appear as polygonal.


3 Simulation 61

3.1.4 Services between Detectors

The services (cooling pipes, power tapes and cables, readout cables and fibres, and patch pan-els) which will occupy the spaces between the three Inner Detector subdetectors are simulatedseparately from the subdetector themselves. The total material contribution from these servicesfor all detectors is summed together and represented by volumes of carbon which has had itsdensity adjusted to give a radiation length of 50 cm, for ease of coding.

The following paragraphs summarise the total amounts of material in these services due to eachsubdetector. In all cases, percentages of radiation lengths are given for normal incidence, i.e.perpendicular to the running direction of the cables. The quoted numbers are for one end of theInner Detector; of course, all the same services are repeated at the other end.

The pixel detectors contribute a total of 2.1% X0 at R = 30 cm, |z| = 79 cm. Two thirds of this isdue to barrel services, one third to end-cap services. In both the barrel and the end-cap detec-tors, 43% of the service material is due to power cables; 51% is due to cooling pipes and fluids;6% is due to optical readout fibres and temperature sensor cables.

Each layer of the barrel SCT detector contributes, at its nominal radius, 0.55% X0 due to coolingpipes and fluids, and 0.37% X0 due to power tapes. The contribution from optical readout fibresis negligible (of the order of 0.003% X0.)

The flange at either end of the TRT barrel is represented as a wheel at |z| = 77 cm, extendingfrom R = 55 cm to R = 108 cm, with a thickness of 7% X0 at normal incidence. Exiting this flangeare the TRT barrel services, increasing from nothing at its inner radius to 1% X0 at its outer radi-us.

The barrel TRT patch panel is represented as an 8 cm wide tube, with a thickness of 12% X0, andhaving a 1 cm wide denser middle section (15% X0), rotated uniformly in φ. The R-z centroid ofthe panel is at R = 112 cm, |z| = 75 cm. Two similar patch panels are placed nearby to represent

Table 3-13 TRT material as a function of |η| (longitudinal vertex spread is included).

Radiation length (%)

|η|=0.0 |η|=0.6 |η|=0.9 |η|=1.2 |η|=1.78 |η|=2.2

Wires (plus wire-joints for barrel) 3.4 0.2 0.2 0.1 0.2 0.1

Gas 0.6 0.7 0.6 0.7 0.7 0.6

Straw walls 4.0 4.9 3.7 4.4 4.2 3.7

Radiator 3.8 4.3 5.1 6.6 8.4 5.6

Barrel-module shells + barrel cylinders 4.3 4.5 2.3

Barrel end-flange + services 1.8 10.2 0.7

Inner end-cap enclosure 2.7 4.6

Outer end-cap enclosure 7.1 9.0 15.4

Outer services (barrel and end-cap) 0.3 2.4 4.9 8.0

Total 16.1 16.9 31.6 29.3 41.6 9.9


62 3 Simulation

the patch panels for the barrel SCT and pixel services. After exiting the patch panel, the barrelSCT and pixel services continue to run between the end-cap TRT and the calorimeter atR = 115 cm.

The TRT end-cap services increase from noth-ing at the start of the detector to 3.9% X0 at theend of the detector. They too are positionedbetween the TRT and the calorimeter atR = 115 cm. A patch panel for the end-cap TRTservices, similar to those described above forbarrel services, is situated at R = 121 cm,|z| = 339 cm. This patch panel is 12 cm wide;the less dense portion is 40% X0, and the 1 cmwide denser inner region is 50% X0.

Each SCT wheel contributes 0.78% X0 due tocooling pipes and fluids, and 0.49% X0 due topower tapes. These services are routedthrough a crack in the TRT at |z| = 278 cm, af-ter which they join the rest of the services atR = 115 cm.

Figure 3-9 shows a detailed view of the crackregion between the barrel and end-cap SCTdetectors. Note that the thickness of the mate-rial decreases, in a step-wise fashion, as R in-creases, to simulate the spreading of cablesand pipes to take advantage of the largeramount of space available as R increases. Foreach ‘step’ in R, the total amount of materialbetween the minimum and maximum valuesof R for that step has been averaged over thestep, producing volumes which are rectangu-lar in cross-section. A volume with smoothlydecreasing thickness would have been moreaccurate but more difficult to describe inGEANT because at the same time more materialis being added as services leave the detectors

3.1.5 Differences between Engineering and Simulation Layouts

Inevitably, there are certain differences between an engineering design and a model for simula-tion. These approximations are apparent from previous sections and will not be discussed here.The simulation model is based on the designs proposed in September 1996, and as a result ofon-going work, the layout presented in the second volume of this report is slightly different.This is generally true of the estimates of the amounts of material which have been modified bymore detailed designs. In future work, the material simulated will be updated. The differenceswhich would affect the simulation model are summarised below.

Figure 3-9 Detail of services in crack between barrel(left) and end-cap (right).


3 Simulation 63

3.1.5.1 Pixels

The following modifications are being considered:

• Changing the module dimensions.

• Changing the tilt angle to between −18.5 and −20.5°. This tilt is in the opposite sense to thecurrent tilt so as to compensate the Lorentz angle and hence reduce the mean clusterwidth in Rφ.

• Inclining the modules with respect to the z-axis by 1.25°.

• Increasing the |z| coverage of barrel layer 2 to 13 modules.

• Decreasing the radial coverage of the disks.

A simple grid of pixels rather than the bricked pixels have been simulated and the big pixels, cor-responding to the gap between the electronics chips, are not simulated. These are issues for thedigitisation, discussed in Section 3.5.

3.1.5.2 SCT

The shape and placement of the electronics board in the simulation differs from the baseline de-sign. However, as the simulation provides sensitive silicon in the right quantities and places,and the amounts of material in the simulation agreed with engineering predictions when aver-aged over φ, it is believed that this difference from the baseline design will have very little or noeffect on the results of the studies presented here.

The inner rings of the SCT used in the simulation consist of GaAs, whereas the current designuses silicon detectors. The simulation of the geometry is the same as will be used for silicon infuture studies, except that the material represented by the GaAs modules is significantly great-er. However, this does not have a huge effect on the results presented from the simulations,since forward going tracks tend to cross just one of the inner SCT rings.

3.1.5.3 TRT

The barrel TRT will be made of trapezoidal modules. These have not been simulated, but allow-ance has been made for the additional material contained in the module walls, as was describedin Section 3.1.3.1.

3.1.5.4 Services

In the current simulation, services are routed in between the fourth and fifth TRT wheels. In theengineering design, they are routed between the third and fourth wheels, although this maychange once the sub-system integration is engineered in detail.


64 3 Simulation

3.2 Magnetic Field

The ATLAS solenoid is 5.3 m long, compared with the 6.7 m length of the tracking volume ofthe Inner Detector. Consequently, the field deviates significantly from uniformity [3-2]. Maps ofthe field are shown in Figures 3-10 and 3-11. It can be seen that Bz falls to about 1.0 T at the endof the solenoid and 0.4 T at the end of the tracker. BR only becomes important for |z| > 2 m,with a maximum of about 0.6 T at the coil aperture.

The consequences of the deviation of the solenoidal field from a uniform Bz = 2 T are:

• Distortion of tracks from perfect helices. This is such that for tracks at large |η|, thebending seen in the transverse projection changes sign. This makes pattern recognitionand track fitting technically more difficult to implement.

• Reduced bending power. Since for high pT, , if the effective radial rangeRmax over which the field is uniform is reduced, the pT resolution is degraded.1 This effectis less significant for the other track parameters, since they have a weaker dependence onRmax.

• Lorentz angle effects in the end-cap silicon detectors. This causes displacement of coordi-nates in the Rφ direction which must be corrected. Unlike the shifts in the barrel, the mag-nitude of these corrections will vary with position.

• Lorentz angle effects in the end-cap TRT. The drift distance-to-time relationship will varywith position.

Despite the significance of the non-uniformity of the solenoidal field, almost all simulations per-formed so far have been with a uniform field, since this is much more straightforward for pat-tern recognition. It is anticipated that the changes to cope with a non-uniform field will be

1. This arises from the sagitta measurement. The true situation is even worse because the effective numberof measurements is reduced and this produces additional degradation like √Neff.

Figure 3-10 Bz as a function of z and R. Figure 3-11 BR as a function of z and R.

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technicalities (albeit quite complicated ones). Since the effect is expected to be most significantfor pT resolution, this has been explicitly studied by a simple simulation, and the results are pre-sented in Section 4.1.

3.3 Rapidity Coverage

The specification (B1) on the number of precision hits (space-points) is ≥ 5 for |η| ≤ 2.5 and thisshould be satisfied for the complete lifetime of ATLAS. To allow for detector inefficiencies, thelayout of the precision detectors was designed so that a stiff track would cross ≥ 2 pixel layersand ≥ 4 SCT stereo layers. Allowance was made for tracks coming from up to ±2 σ from z=0. Inaddition, the B-layer will provide an extra space-point for as long as is technically feasible.

To understand the purely geometrical effects, the number of hits per tracks has been determinedusing stiff tracks, with no vertex spread and no detector inefficiencies. The results are shown inFigures 3-12 and 3-13. While the design of the SCT detectors to provide space-points fromsmall-angle stereo is important to reduce fake tracks and provide simpler pattern recognition,the pattern recognition algorithms currently used do not have a strong dependence on the exist-ence of space-points per se. The geometrical overlap between the two sets of strips in an SCTmodule is about 95%. However, for simplicity, the figures show the sums of Rφ and stereo hitsfor the SCT (the number of each is the same because of the identical nature of the Rφ and stereodetectors).

Since the B-layer provides complete coverage over |η| with no major gaps, it provides one pix-el space-point for all η. By design, there is an increasing number of precision hits at large |η| tocompensate for the loss of bending power and to cope with the non-uniformity of the solenoidalmagnetic field. The variations in the number of TRT straws crossed are related to the geometry(dead region around z = 0 and gap in barrel/end-cap transition region) and the regions of dif-ferent straw density in the end-caps.

Figure 3-12 Number of hits seen by a stiff track fromz=0 in pixels and SCT (perfect efficiency).

Figure 3-13 Number of hits seen by a stiff track fromz=0 in TRT (perfect efficiency).

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The same distributions allowing for the default silicon efficiencies of 97% and standard spreadin collision point of σz = 5.6 cm are shown in Figures 3-14 and 3-15 (stiff tracks) and Figures 3-16and 3-17 (pT = 1 GeV tracks). The vertex spread tends to smear out the distributions shownabove. The ‘error bars’ on the plots indicate the r.m.s. spread of the numbers of hits. The spreadis the result of random inefficiencies and small overlaps in the precision layers and the fact thatthe straws in the TRT are not close-packed. It can be seen that there is relatively little differencefor the precision layers between the distributions for high and low pT tracks, since the layouthas been designed to be hermetic down to pT = 1 GeV.

Figure 3-14 Number of hits seen by stiff track in pix-els and SCT.

Figure 3-15 Number of hits seen by stiff track in TRT.

Figure 3-16 Number of hits seen by pT = 1 GeV trackin pixels and SCT.

Figure 3-17 Number of hits seen by pT = 1 GeV trackin TRT.

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It can be seen (by combining the pixel hits with half of the SCT hits) that the specification (B1)on the number of precision hits has been met by design. The TRT straws provide ≥ 36 hits overmost of the pseudorapidity coverage, satisfying the specification (B2). In the barrel/end-captransition region and near |η| = 2.5, they provide ≥ 25 hits.

3.4 Material

The requirements on the performance of the ATLAS Inner Detector are more stringent than forany tracking detector ever built for operation at a high-luminosity hadron collider: the environ-ment at the LHC will be particularly harsh because of the required speed of response and radia-tion-hardness of all components and of the large pile-up effects unavoidable at high luminosity.In addition, access to the detector itself will be very limited. It is therefore not a surprise that theamount of material in the active volume of the Inner Detector is much larger than that of previ-ous tracking detectors. This is mostly due to the large η coverage required in the very smallavailable volume and to the necessity of installing all the front-end electronics components onthe detector itself.

The material distribution in the ATLAS Inner Detector has been mapped out by tracking geanti-nos1 through the GEANT description of the detector discussed in Section 3.1. Detailed calcula-tions have been made for most of the complex items in the Inner Detector. However in thesimulation, these items are approximated as simple blocks where the material is matched to themost significant component of the item and the thickness is tuned to describe the average radia-tion length. Therefore the local ‘lumpiness’ of the real detector may have been lost, but the aver-age amount of material seen by any track is well described.

In what follows, the Inner Detector has been split into four parts:

a. Pixels, associated services and supports, and the beam pipe.

b. SCT, associated services and supports, and services passing through.

c. TRT, associated services and supports, and services passing through.

d. Services and supports external to the sensitive volume of the Inner Detector, includ-ing the patch panels at R ≈ 100 cm, |z| ≈ 90 cm and R ≈ 120 cm, |z| ≈ 340 cm.

The material distributions have been derived for the tracking volume: R ≤ 115 cm and|z| ≤ 340 cm. Inner Detector services run up the vertical crack between the calorimeter barreland end-caps, and so present material in front of the end-caps. For most of their length, theseservices are not the most significant source of shadowing of the end-caps. However, the secondset of patch panels (with ~0.35 X0 around |η| ≈ 1.8) do cause serious shadowing of the calorim-eter and have been included in the calculations.

1. Hypothetical, neutral, non-interacting particles used by GEANT to describe straight rays through a de-tector volume.


68 3 Simulation

3.4.1 Radiation Lengths

3.4.1.1 Distributions

The distributions for the number of radiation lengths for the four parts of the Inner Detector areshown in Figure 3-18. Features which deserve note are:

a. Services from pixels in ‘dog-leg’ starting at |η| = 1.4.

b. Services from pixels and SCT in barrel/end-cap crack starting at |η| = 1.1.

c. Services from pixels, SCT and TRT in barrel/end-cap crack and TRT flange startingat |η| = 0.7, with services from SCT in crack at end of SCT end-cap at |η| = 1.7.

d. Patch panels at |η| = 0.7 and 1.7.

Figure 3-18 Number of radiation lengths for a) Pixels, associated services and supports, and the beam pipe,b) SCT, associated services and supports, and services passing through, c) TRT, associated services and sup-ports, and services passing through and d) Services and supports external to the sensitive volume of the InnerDetector, including the patch panels.

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The cumulative distributions are shown inFigure 3-19. The amount of material is sub-stantially larger than that simulated at thetime of the ATLAS Technical Proposal [3-3].The changes reflect the increasingly realisticdetector descriptions which have been imple-mented in the simulation. The amount of ma-terial in the SCT/pixel precision layers issimilar to that in the TRT, but is by design con-centrated at low radii, thereby causing themost damage to some aspects of the calorime-ter and Inner Detector performance, as dis-cussed in [3-4] and below. The top part of thecurve in Figure 3-19 corresponds to the servic-es and patch panels at large radius, i.e. outsidethe active tracker volume; although they con-tribute a sizeable fraction of the total Inner De-tector material, their impact on theperformance is small, since they are situatedjust in front of the much larger amount of ma-terial contained in the cryostats and the sole-noidal coil.

The average up to and including the TRT (but not external services) over the range |η| ≤ 2.5 is43% X0, and peaks at ~60% X0 in the worst region around eta = 1.8.

3.4.1.2 Consequences

The consequences for the calorimeter of this large amount of material in the Inner Detector aresignificant [3-4]. For the Inner Detector, the consequences are also important:

• Tracks undergo significant multiple scattering - apparent from Chapter 4.

• There is a significant increase in multiplicity from secondary particles (mainly the conver-sions of photons from π0’s) - apparent from this chapter.

• Electrons have a significant bremsstrahlung probability - discussed in Section 6.1.

• Photons have a significant conversion probability - discussed in Section 6.3 for isolatedphotons and in Section 6.7 for photons in jets.

Figure 3-19 Cumulative distribution for number ofradiation lengths for (a) pixels, (b) SCT, (c) TRT and(d) external services and patch-panels. Correspondsto Figure 3-18.

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70 3 Simulation

The conversion probability for photons isshown as a function of |η| for different radialranges in Figure 3-20. The average over |η| is~30% for conversions before the external serv-ices of the Inner Detector (R < 110 cm). ForpT > 1 GeV, the distributions reflect thenumber of radiation lengths of Figure 3-18(probability is 1−exp(−7/9 x/X0) where x/X0is the number of radiation lengths). The con-version probability varies little with pT forpT > 1 GeV, but falls significantly for verylow-pT.

With an average of 9.5 photons havingpT > 1 GeV in a b-jet (see Section 2.4.3), thereare a significant number of conversion elec-trons in a jet, the consequences of which arediscussed in Section 6.7. Figure 3-20 Photon (pT > 1 GeV) conversion proba-

bility for different conversion radii Rc: 0 < Rc ≤ 20 cm(dotted), 20 < Rc ≤ 60 cm (dashed), 60 < Rc ≤ 110 cm(solid).

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3.4.2 Absorption Lengths

Not only does the amount of material in the Inner Detector represent a significant fraction of aradiation length, but the amount of material leads to a significant probability for interactions ofprimary hadrons.


The distributions for the number of absorption lengths for the four parts of the Inner Detectorare shown in Figure 3-21.

Figure 3-21 Number of absorption lengths for a) Pixels, associated services and supports, and the beam pipe,b) SCT, associated services and supports, and services passing through, c) TRT, associated services and sup-ports, and services passing through and d) Services and supports external to the sensitive volume of the InnerDetector, including the patch panels.

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The cumulative distributions are shown inFigure 3-22. The average up to and includingthe TRT (but not external services) over therange |η| ≤ 2.5 is 0.14 absorption lengths.

3.4.2.2 Consequences

The consequences for the Inner Detector of thenumber of absorption lengths are:

• Absorption of hadrons, causing tracksto be lost.

• Hadrons undergoing large scatters orprimary and secondary tracks beingmerged in reconstruction. These effectscause tails in impact parameter distribu-tions, which affect b-tagging - discussedin Section 6.7.

• Increase in multiplicity from secondaryparticles.

These consequences have been studied with decays using mH = 400 GeV. These eventsproduce a spectrum of pions: those coming from the primary vertex have a mean pT of 1.5 GeV,while those from the b decays have a mean pT of 10 GeV and a multiplicity of 4.7 pions perB-meson decay.

Figures 3-23 and 3-24 show the positions of the interaction points of pions in the Inner Detector.Points not associated with subdetector layers correspond to interactions in the gas-filled vol-ume of the detector.

Figure 3-23 Position of interaction points of pions inInner Detector in x-y.

Figure 3-24 Positions of interaction points of pions inInner Detector in R-z.

Figure 3-22 Cumulative distribution for number ofabsorption lengths for (a) pixels, (b) SCT, (c) TRT and(d) external services and patch-panels. Correspondsto Figure 3-21.

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Figure 3-25 shows the charged particle multi-plicity of tracks originating at the chargedpion interaction vertices in the Inner Detector.The mean multiplicity is 4.1, although only14% have pT > 1 GeV.

Figure 3-26 shows the interaction probability as a function of |η|. This rises from 8% to greaterthan 20% around |η| = 1.7 and reproduces the shape of the distribution of the number of ab-sorption lengths in Figure 3-22. The probability as a function of pT is fairly flat and is shown inFigure 3-27.

Figure 3-26 Pion interaction probability as a functionof |η|.

Figure 3-27 Pion interaction probability as a functionof pT.

Figure 3-25 Number of charged secondaries comingfrom pions interacting in the Inner Detector.

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Figure 3-28 shows the probability for recon-structing a primary pion from a b-jet as a func-tion of its interaction radius, averaged overthe pseudorapidity distribution of the tracks.Also shown is the probability of reconstruct-ing a secondary pion (pT > 1 GeV) as a func-tion of its production radius.

As a consequence of the distribution of materi-al in the tracking volume and the reconstruc-tion probability shown in Figure 3-28 theprobability for track which interacts anywherein the volume to be reconstructed is about halfof that for non-interacting tracks.

3.5 Pixels

The layout details of the pixel subdetector were set out in Section 3.1. In this section, explana-tion is provided as to how signals are simulated in the devices and the consequences for the ex-traction of coordinates are given.

A simple orthogonal grid of pixels (each 50μm×300μm) is used in the standard simulation forsimplicity. The simulated r-z resolution is somewhat worse than that expected for the brickedpixels, and the loss in resolution for the small fraction of special big pixels at the edge of theelectronics chips is not taken into account.

3.5.1 Digitisation

The response of a hit pixel is calculated from the GEANT hits in the sensitive volume of the sili-con crystal where at least 5 hits with 3-D coordinates are recorded. Each of these hits has an en-ergy distributed according to the Landau distribution. Each energy deposit is converted into anumber of electron-hole pairs using a factor of 2.67×102 pairs/keV. Subsequently, the chargerepresented by the hits is divided into 20 equal cluster-charges positioned in space along thetrack around the GEANT hit. The clusters are projected into the corresponding pixels allowingfor the Lorentz angle shift, tanω = −0.2792 (applied only in the Rφ direction for the barrel crys-tals) and the diffusion spread of σdif = 7 μm , where d is the distance to the elec-tronic side of the crystal.

Figure 3-28 Reconstruction probability for a) primarypions (solid) as a function of interaction radius and b)secondary pions (dashed) as a function of creationradius (pT > 1 GeV).

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The standard cutoffs used by ATLAS in thetracking of low energy secondaries are100 keV for photons and charged particles and1 MeV for δ-ray, conversion pairs and bremsst-rahlung photon production. Decreasing thesecutoffs to 10 keV, some degradation in the per-formance is observed. This is illustrated inFigure 3-29, where the impact parameter reso-lution (which will be discussed more com-pletely in Section 4.4) is seen to degrade byabout 1 μm.

The typical energy deposition by a relativisticparticle crossing the full detector at normal in-cidence corresponds to 13000 electrons. AGaussian random fluctuation of 200 electronsr.m.s. is added to the signal. The pixel is con-sidered to be ‘hit’ if the accumulated charge isabove a threshold, which has a mean value of2000 electrons and an r.m.s. of 400 electrons.Signals below threshold are kept in the outputDIGI banks, but flagged such, allowing thepossibility to change the threshold after the simulation has been completed.

3.5.2 Simulation of Noise and Inefficiency

As well as resulting from signals belowthreshold, inefficiencies also arise for technicalreasons: dead electronic cells, bad bondingcontacts or pixels masked because they arenoisy. At present a random inefficiency of 3%is applied to all pixels in a module.

The electronics noise is generated only in thepixel detector modules which have at least onehit from particle tracks. It is assumed, that thenoisy hits in the empty detectors are too farfrom tracks to give any sizable perturbationsto pattern recognition. The default noise levelin the pixel detectors, corresponding to thestandard threshold of 2000 electrons is set to10−5, which can be achieved after hardwaremasking of the noisy pixel detectors. In orderto study the performance with higher noiselevel the standard datasets also contain be-low-threshold noise hits with probability 10−4,which can be activated by lowering the thresh-old. Figure 3-30 shows how the expected noiseand inefficiency degrade the impact parameter resolution from what would be seen for perfect

Figure 3-29 Effect of simulation of δ-rays on impactparameter resolution (200 GeV muons): standard sim-ulation (solid circles) and δ-rays down to 10 keV (opencircles).

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Figure 3-30 Effect of noise and inefficiencies onimpact parameter resolution (200 GeV muons): nonoise and 100% efficiency (open circles) and standardsimulation (solid circles).

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76 3 Simulation

pixel detectors. The largest effect comes from inefficiencies where part of a cluster is lost; it isvery unlikely that there is absolutely no cluster observed in the B-layer.

3.5.3 Rapidity Coverage and Properties of Clusters

A sample of high-pT muons, flat in the interval −2.5 ≤ η ≤ +2.5 and with a realistic vertex spreadwas used to study the coverage of the pixel detectors. Figure 3-31 shows the mean number ofpixel modules crossed. The change-over from barrels to disks is clear in the region 1.5 ≤ |η| ≤ 2,while the B-layer covers the complete η range. The mean tends to exceed the number of layerssince, within the layers, there are overlaps.

Figure 3-31 also shows the mean number of pixels above threshold. By design the detectors areorientated to spread the charge over a cluster of several pixels to improve the resolution. It canbe seen that at η = 0, there are twice as many pixels above threshold as there are modulescrossed. In the barrel, this ratio increases with |η|, as the charge is spread in z over more pixels.This is seen in Figure 3-32, which shows the width of the clusters. Since tracks hit the disks closeto normal incidence, there are no tilts and no significant Lorentz effects, clusters in the diskstend to consist of single pixels. The intention of spreading the charge by tilting the barrel detec-tors is to improve the Rφ resolution. It turns out that mean cluster widths of 2 are not so good -the optimal width is ~1.5. Also the two-hit resolution is less good. This is being improved inmore recent designs, as was explained in Section 3.1.5.

Figure 3-31 Mean number of pixel modules crossedand the mean number of pixels above threshold as afunction of pseudo-rapidity: barrel (solid circles), disks(open circles).

Figure 3-32 Mean cluster width in pixels in Rφ andR/z directions: barrel (solid circles), disks (open cir-cles).

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3 Simulation 77

3.5.4 Spatial Resolution

The spatial resolution has been estimated as the r.m.s. of the residuals between the positionwhere a muon cross the centre of a silicon detector wafer and the centroid of the correspondingpixel cluster, evaluated in the local coordinate system of the module. These residuals are shownin Figures 3-33 and 3-34. Because of charge sharing, the residuals in the barrel layers are close toGaussian. Clusters in the disks are dominated by single pixels giving flat distributions; exceptfor narrow regions close the edges of the pixels where there is charge sharing between adjacentpixels, giving spikes in the residual distributions.

In the barrel, there is a 20 μm shift in Rφ due to the Lorentz angle. Some small biases of the orderof 1 to 3 μm arise due to asymmetric effects of the electron diffusion in adjacent pixels, which isa function of the angular distribution of the tracks under consideration.

The resolution of the coordinates derived from the cluster centroids are shown in Figures 3-35and 3-36. In the barrel, the Rφ measurements improve with increasing |η| due to the increasedcharge sharing. However, this is only true in z up to |η| ≈ 1.1, beyond which, the clusters be-come very long in z, due to the large incidence angle in the R-z plane.

The means of the resolutions, averaged over a flat pseudorapidity distribution, are:

• Mean σ(Rφ) = 12 μm.

• Mean σ(z) in barrel = 66 μm.

• Mean σ(R) in disks = 77 μm.

Bricked PixelsIt is clear from Figure 3-36 that the z resolution in the pixels is much worse than that in Rφ sincethe pixels cells are six times longer than they are wide. By arranging the pixels in the so-calledbricked design, where they are arranged in rows in z, each row being offset by half a pixel (i.e.150 μm), charge sharing improves the z resolution for |η| < ~0.8. Figures 3-37 and 3-38 showthe resolutions expected for the bricked design.

Figure 3-33 Pixel residuals in Rφ (upper: barrel,lower: disks) averaged for tracks flat in |η|.

Figure 3-34 Pixel residuals in z (upper: barrel) and R(lower: disks) averaged for tracks flat in |η|.

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78 3 Simulation

3.5.5 Occupancy

One of the important features of the pixel detectors is their low occupancy. Using the particledensities presented in Figure 2-6, it is easy to see that the occupancies of the pixel cells in theB-layer is of the order of 10-3 at a luminosity of 1034 cm-2s-1 (3×10-4 particle occupancy multi-plied by cluster sizes of 2 to 4). In this section, occupancies are shown corresponding to pile-upat 1034 cm-2s-1 and to b-jets from with mH = 400 GeV. For the pile-up sample, the plotsrepresent the average occupancy - averaged over all modules in the relevant η range. For thesample containing b-jets, the worst case occupancy is presented by studying the hit distribution

Figure 3-35 Resolution in Rφ for pixel barrel (solid cir-cles) and disks (open circles).

Figure 3-36 Resolution in z for pixel barrel (solid cir-cles) and R for disks (open circles).

Figure 3-37 Resolution in Rφ for pixel barrel withbricked pixels.

Figure 3-38 Resolution in z for pixel barrel withbricked pixels.

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3 Simulation 79

in the highest occupancy module for each SCT layer. Only modules which lie within the core ofthe b-jet, ΔR < 0.2, are considered for this study.

In this section, a hit corresponds to a single fired pixel cell. A cluster is made up a set of hitsconnected by an edge or a corner. In subsequent chapters of this report, the reconstructed clus-ters which form coordinates are referred to as ‘hits’. To provide more useful numbers for thestudy of occupancy, a more up-to-date geometry has been used for the pixel modules. This al-lows for the gaps between the chips, where the bonding of the electronics to the pixels is morecomplicated. Also two of the end-cap detectors described in Section 3.1.1.2 are combined in onemodule, doubling the active area of one module. Consequently, the numbers of pixels in a barreland end-cap modules are 61440 and 56448, respectively.

The effects seen as a function of R and |η| can be explained by the facts that i) the density ofparticles in pile-up is fairly uniform in η−φ, ii) for the jets, the particles are highly collimated, sothat many of the tracks of one jet will cross a single module, iii) modules at higher |η| cover asmaller Δη and iv) cluster sizes in the barrels increase with |η|.

3.5.5.1 Occupancy per Column

One of the most important considerations for the occupancy is the number of hits in a pixel col-umn1, since this places restrictions on the electronics architecture and defines the size of thebuffers. Examples of these distributions are shown in Figures 3-39 and 3-40. The occupanciesare peaked at very low values - most columns are empty.

1. A pixel column is a column of 164 pixels in the Rφ direction across half the width of a pixel module.

Figure 3-39 Number of hits per column for pixelbarrel 0 (B-layer).

Figure 3-40 Number of hits per column for inner pixeldisks.

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80 3 Simulation

The variation with |η| of the mean occupan-cy per column for pixel detectors placed at dif-ferent radii is shown in Figure 3-41.

BarrelsLarge occupancies are observed in some col-umns (see Figure 3-39); these come mainlyfrom loopers, whose trajectories may cross thepixel detectors at very small angle, causingmany pixel cells to fire. This is of crucial im-portance in fixing the buffer size for the elec-tronic readout, since loopers may wash outcompletely the buffer, removing valid hitsfrom other beam-crossings.

While the mean occupancy decreases quadrat-ically as the layer radius increases, as expectedfrom solid angle considerations, the number ofcolumns per event with large occupancy re-mains constant.

DisksFor the disks, a clear distinction can be made between the 3 inner disks (those with the inner ra-dius at 11 cm) and the 4 outer disks (with inner radius at 16 cm).

3.5.5.2 Occupancy per Module

The number of hits per module to be read out determines the readout time. The mean numberin each of the different modules is shown in Figures 3-42 and 3-43. Summaries of this informa-tion are provided in Table 3-14.

Figure 3-42 Mean number of hits per pixel module forpile-up.

Figure 3-43 Mean number of hits per pixel module forb-jets.

Figure 3-41 Mean number of pixel hits per column forpile-up events.

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3 Simulation 81

3.5.5.3 Cluster Width and Fraction of Merged Clusters

The size and separation of clusters is important for pattern recognition. The cluster widths, av-eraged over all clusters, do not depend strongly on the event type. The mean cluster widths,arising from tracks of all pT in pile-up and including noise hits are shown in Figures 3-44and 3-45. They are very similar to the distributions seen for high-pT tracks in Section 3.5.3, al-though there is an indication of more charge sharing in the disks, which explains the differencesbetween the occupancies of the disks seen in Figures 3-42 and 3-43.

The number of clusters per module as function of |η| is plotted in Figures 3-46 and 3-47.

It is not straightforward to discuss two-hit separation in a 2-D detector. Rather it is more inter-esting to examine the number of merged clusters, where a single cluster has contributions fromtwo or more charged tracks. This is particularly important in the B-layer, since the merging ofclusters may generate false impact parameters. Given one cluster in the B-layer, the probabilitythat this will be merged with a cluster arising from a pile-up track can be calculated as the areato isolate the first cluster multiplied by the occupancy1 from pile-up. The distance required toseparate clusters in each projection is approximately twice the cluster half-width plus one pixel.For |η| = 0, this corresponds to about 6 pixels, giving a probability of merging of the order

Table 3-14 Average number of hits per module and occupancies for pixel layers.

Pile-up b-jets

Num hits Occupancy Num hits Occupancy

Barrel 0 (B-layer) 26.9 4.4 × 10-4 27.4 4.5 × 10-4

Barrel 1 5.4 0.9 × 10-4 18.9 3.1 × 10-4

Barrel 2 3.7 0.6 × 10-4 19.1 3.1 × 10-4

Inner Disks 2.7 0.5 × 10-4 6.6 1.2 × 10-4

Outer Disks 2.9 0.5 × 10-4 6.6 1.2 × 10-4

Figure 3-44 Mean Rφ pixel cluster width for pile-up. Figure 3-45 Mean z/R pixel cluster width for pile-up.

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82 3 Simulation

of 10-3. The fractions of merged clusters are shown in Figures 3-48 and 3-49. It can be seen thatthe number of merged clusters is not very large and will be reduced further when the tilt of themodules is changed. Nevertheless, as will be seen in Section 3.5.5.3, the rate of merging in thepixels for tracks in jets is compatible with that found in the SCT strips. The consequences of thisare examined in Section 5.2.

1. More correctly, this is the particle occupancy, defined as the flux of charged particles per pixel. This differsfrom the normal occupancy by a factor equal to the cluster size.

Figure 3-46 Mean number of pixel clusters per mod-ule for pile-up.

Figure 3-47 Mean number of pixel clusters per mod-ule for b-jets.

Figure 3-48 Fraction of merged clusters for pile-up. Figure 3-49 Fraction of merged clusters for b-jets.

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3 Simulation 83

3.6 SCT

The layout details of the SCT subdetector were set out in Section 3.1. In this section, explanationis provided as to how signals are simulated in the devices and the consequences for the extrac-tion of coordinates are given.

3.6.1 Simulation of Signal and Digitisation

The simulation of signals and their subsequent digitisation in the SCT is similar to that in thepixel detectors. In the simulation phase, GEANT divides each track into 80 μm segments. The en-ergy deposited in each of these track segments is translated into the number of electron-holepairs produced in the active volume of the semiconductor. For silicon modules, 2.76×102 elec-tron-hole pairs are created per keV of deposited energy; for GaAs modules, 1.81×102 pairs/keVare created. To make the simulated response agree better1 with test-beam results, the transverseposition of the deposited energy is smeared, on a track-by-track basis, by a Gaussian of width12 μm.

For Silicon detectors, diffusion of the charge in the semiconductor volume is simulated by as-suming that it will have a Gaussian profile perpendicular to the strips. The width of the spreadis determined by the track angle, a diffusion constant, and in the barrel, the Lorentz angle. ForGaAs detectors, the charge is divided between adjacent strips only if the midpoint of the tracksegment lies in a gap between strips, in which case the fraction of the total charge assigned toeach strip is inversely proportional to the distance between the edge of the strip and the hit po-sition.

Electronics crosstalk can be simulated by assigning each strip a certain fraction of its owncharge plus some fraction of the charge on its nearest neighbour strips. By default, this crosstalkis turned off as part of the tuning process to make the simulated response agree with test-beamresults.2

An inefficiency of 3% is applied randomly to all strips in a module through which a track haspassed. Noise in the electronics is simulated by adding charge to each strip according to a Gaus-sian distribution with a sigma of 1875 electrons.

Only those strips which are above a threshold are included in the digitisation output. The de-fault threshold for keeping a simulated digit is 2.6 times the width (σ) of the noise distribution,which gives a (pessimistic) noise-occupancy level of 0.5%. However any digits which lie below3.5σ are flagged as being below standard threshold and by default are ignored in the reconstruc-tion phase. This higher threshold gives a noise occupancy at the level of 10-4, as observed in testbeam studies. By using this dual threshold scheme, additional noise may be considered in thereconstruction, if required.

For the SCT binary electronics, no pulse-height information will be recorded for fired strips, butonly the fact that they were above threshold. In the simulation, the pulse-heights are digitisedand stored along with the strip position and the noise, threshold and inefficiency flags.

1. Without this smearing the Rφ resolution in the simulation is too good compared to test-beam results.2. In particular to describe the mean cluster width


84 3 Simulation

3.6.2 Cluster Widths

Figures 3-50 and 3-51 show the number of strips fired per track or cluster width forpT = 200 GeV muons in the SCT barrel and end-caps, respectively. The mean cluster widths are1.22 and 1.13, respectively.

3.6.3 Spatial Resolution

The Rφ track residual is calculated as the difference in Rφ between where a track has crossed thecentre (thickness-wise) of a silicon wafer and the centroid of the resulting cluster of strips. Thecorresponding resolution is the r.m.s. of the residual distribution. Figures 3-52 and 3-53 showthe distributions of residuals in the SCT barrel and end-caps, respectively. The correspondingresolutions are 22 μm and 24 μm, respectively. While the cluster width will be larger for low-pTtracks as a consequence of the reduced angle of incidence, and hence the resolution will de-grade slightly, this effect is negligible compared to the effect of multiple scattering. The varia-tions of the mean cluster width and the resolution with |η| are shown in Figures 3-54and 3-55.

Space-points (Rφ,z) or (Rφ,R) within one module of the SCT can be formed from the combina-tion of an Rφ and a stereo measurement. While it is the individual measurements which areused for the final fit, space-points are used in the initial phase of iPatRec as well as in the Lev-el-2 trigger algorithms. The effective combination of a hit in each of the two layers of a moduledefines a parallelogram whose axis is rotated by half the stereo angle (α). If each plane has a po-sition resolution σ1, for small α, the effective resolution of the combination is σ1/√2 in Rφ and√2σ1/α in z (or R). However, the rotation of the error ellipse is significant, and in the presence ofseveral other Rφ measurements, the effective resolution in z (or R) becomes σ1/α [3-5], which isabout 580 μm for the SCT barrel.

Figure 3-50 Cluster widths in SCT barrel. Figure 3-51 Cluster widths in SCT end-caps.

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3 Simulation 85

3.6.4 Comparison with Test-beam Results

To compare the response from the simulation with that of real detectors in test-beam, a modifiedsimulation was performed where the physical parameters of the simulated detectors (e.g. strippitch) and experimental layout (e.g. angle of incidence of the tracks) were matched as closely aspossible to the test-beam conditions. Figures 3-56 and 3-57 show the residuals and clusterwidths respectively from the simulation, overlaid with the corresponding plots from thetest-beam, for tracks incident on the detectors at the Lorentz angle of 12°. Figures 3-58 and 3-59show the means of the same quantities for simulated and test-beam data as a function of the an-gle of incidence. Reasonable agreement is observed, since the parameters of the simulation havebeen adjusted to describe precisely these distributions.

Figure 3-52 Residuals in SCT barrel. Figure 3-53 Residuals in SCT end-caps.

Figure 3-54 Mean cluster width in SCT barrel as afunction of |η|.

Figure 3-55 Resolution in SCT as a function of |η|.

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86 3 Simulation

3.6.5 Occupancy

Occupancies in the SCT have been studied using the same Monte Carlo data samples describedin Section 3.5.5. For the pile-up sample, the plots represent the average occupancy - averagedover all modules in the relevant η range. For the sample containing b-jets, the worst case occu-pancy is presented by studying the hit distribution in the highest occupancy module for eachSCT layer. Only modules which lie within the core of the b-jet, ΔR < 0.2, are considered for thisstudy. In referring to ‘modules’, only the 768 Rφ strips are considered; the stereo strips in thesame module have the same occupancies.

Figure 3-56 Cluster widths: comparison of test-beamdata with simulation from DICE.

Figure 3-57 Residuals: comparison of test-beam datawith simulation from DICE.

Figure 3-58 Mean cluster width (in numbers of strips)as a function of detector tilt angle: comparison oftest-beam data with simulation from DICE.

Figure 3-59 Resolution as a function of detector tiltangle: comparison of test-beam data with simulationfrom DICE.

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3 Simulation 87

In all cases, a hit is defined to be a single fired strip. A cluster is defined to be a set of contiguoushits in a single module. In subsequent chapters of this report, the reconstructed clusters whichform coordinates are referred to as ‘hits’.

3.6.5.1 Occupancy per Module

Figures 3-60 and 3-61 show representative occupancy distributions for the two classes of events,described above. It is extremely rare to find events where modules have occupanciesabove 10%. Figures 3-62 and 3-63 show the mean number of hits per module as a function of|η| for different SCT layers, and the results, averaged over η are summarised in Table 3-15. Forthe pile-up events, the occupancy scales with the area (in η−φ) subtended by the module. Forb-jets, the occupancy is nearly independent of radius since the size of the jet in η−φ is smallerthan the area of a module. In both cases, the mean occupancies are low, a feature that simplifiesthe pattern recognition.

Figure 3-60 Occupancy for SCT barrel 1 in pile-upevents.

Figure 3-61 Occupancy for SCT barrel 1 in core ofb-jets. There is one entry per b-jet within barrelacceptance.

Table 3-15 Average number of hits per module and occupancies for SCT layers.

Pile-up b-jets

Num hits Occupancy Num hits Occupancy

Barrel 1 4.7 6.1 × 10-3 13 1.7 × 10-2

Barrel 2 3.8 4.9 × 10-3 12 1.6 × 10-2

Barrel 3 3.1 4.0 × 10-3 11 1.4 × 10-2

Barrel 4 2.6 3.4 × 10-3 11 1.4 × 10-2

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88 3 Simulation

3.6.5.2 Cluster Width and Fraction of Merged Clusters

Figures 3-64 and 3-65 show the number of strips in a cluster as a function of η for the pile-upand Higgs samples. The means (especially those for pile-up) are higher than those obtainedfrom single high-pT tracks (see Section 3.6.2), since these samples include low momentumtracks which bend in the magnetic field and some of the clusters are merged (see below). Thecluster size depends only weakly on radius and η.

If tracks are close together in Rφ over the area of a module, then the clusters which they producemay merge into a single cluster. Similarly, clusters from tracks may be merged with noise hits.The rate for such merging is shown in Figures 3-66 and 3-67 for pile-up and b-jet events respec-

Figure 3-62 Mean number of hits per SCT module forpile-up.

Figure 3-63 Mean number of hits per SCT module forb-jets.

Figure 3-64 Mean cluster width in pile-up events. Figure 3-65 Mean cluster width in core of b-jets.

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3 Simulation 89

tively. The merging rate decreases with radius in the pile-up sample since the separation be-tween tracks increases. For the b-jet sample, the rate is nearly independent of radius, since thehigh-pT tracks in the core of the jet remain close together even at the outside of the SCT. Thefraction merged in this sample is approximately 2%. (The statistical uncertainty on each of thedata points in Figure 3-67 is roughly ±20% of the merging fraction.)

Figures 3-68 and 3-69 show the fraction of clusters which do not result from primary tracks. Thefraction increases with η as expected from the material distribution in the detector. For both thepile-up and b-jet samples, the secondary fraction increases slowly with radius. In both samples,but especially for the pile-up events, a significant fraction of the secondary clusters originatefrom large angle scattering of particles produced in the beam-pipe.

Figure 3-66 Fraction of merged clusters in pile-upevents.

Figure 3-67 Fraction of merged clusters in core ofb-jets.

Figure 3-68 Fraction of clusters not resulting from pri-mary tracks in pile-up events.

Figure 3-69 Fraction of clusters not resulting from pri-mary tracks in core of b-jet.

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90 3 Simulation

3.7 TRT

3.7.1 Introduction

A straw drift tube measures the distance from a track to its central wire by measuring the time ittakes for the ionisation electron clusters created along the track to drift in to the central wire.The position resolution of a straw tube is determined by how accurately this drift time can bemeasured and how well the position of the straw tube’s central wire is known. These measure-ments are made by recording the leading edge of a signal rising over a threshold and are re-ferred to as drift-time hits. If a leading edge is not available but the threshold is exceeded, a hitstraw’s spatial resolution reverts to its diameter/√12 and the measurement is referred to simplyas a straw hit.

Several effects are reflected in the time which a straw tube measures:

1. Flight time - time between production of a particle and when it crosses a straw.

2. Spatial distribution - of the ionisation clusters.

3. Drift time - time for ionisation clusters to reach the wire.

4. Propagation time - time for signal to reach electronics.

5. Electronic shaping.

An additional complication in understanding how a straw tube measures time occurs whenmore than one track strikes a straw tube within or just before the gate during which the hits arerecorded. Depending on how closely in time multiple tracks strike a straw tube, the leadingedge of the later hits can be obscured by the trailing part of a previous pulse so that the timemeasurement for the later hit is not recorded: this effect is referred to as shadowing.

3.7.2 Time Response Model

The TRT simulation contains a detailed model of how a straw tube and its associated electronicsrespond to charged particle hits. The model reproduces the response of the straw tube even athigh rates. The steps in generating the recorded time for each straw tube are:

1. The ionisation deposited by each track crossing a straw (see Figure 3-70) is calculated us-ing the Photo Absorption Ionisation Model (PAI Model) [3-6][3-7]. This energy is dividedamong a small number (about 13-15) of primary ionisation centres. By using the PAI mod-el, the energy and spatial fluctuations of dE/dx measured in test-beams are fully repro-duced. The hit information also accurately describes the number and energy of theTR photons absorbed by the straw.

2. Using the measured electron drift velocity [3-8], the drift-time of each generated cluster tothe wire is calculated, and then corrected for the flight and propagation times.

3. For each wire, the signal amplitudes and arrival times are recorded, summing over all pri-mary clusters and tracks crossing the straw: this forms the straw output signal.

4. Energy associated with any absorbed transition radiation photons is added to this distri-bution.


3 Simulation 91

5. The straw output signal is convoluted with a model of the electronics signal shape basedon measurements of the response of prototype electronics. A pulse-height versus timedistribution is thus generated for each straw.

6. A low (minimum ionising) threshold of 200 eV and a high (transition radiation candidate)threshold of 5 keV are used to find at which times the low and high thresholds arecrossed. The amplified signal can fail to cross the threshold, cross the threshold once, orcross the threshold more than once.

7. The discriminator response is modelled with a pulse-width equal to the time over thresh-old plus 2 ns (but not shorter than 10 ns) and with a recovery time of 5 ns after the pulsedrops below threshold.

8. The track coordinate is reconstructed using the time of the discriminator leading edgeand the established radius-to-distance relationship (or R-t dependence), as describedin Section 12.2.2.1.

9. The spatial resolution from a single straw is typically 120 μm - which matches test-beamdata. However, it is anticipated that for the real detector, systematics associated with theoverall system performance of the TRT detector will increase this to about 170 μm. There-fore, the cluster arrival time is jittered by ±6 ns to obtain this single straw resolution.

The magnetic field represents a source of uncertainty in the present simulation. The inhomoge-neities in the field at large |η| will result in different drift-times for different regions of the TRTfor comparable hit positions relative to the anode wires. Such effects can be taken care of withproper calibration procedures.

3.7.3 Comparison with Test-beam Results

The main requirement for the simulation model is to reproduce accurately experimental dataobtained under different conditions. In this section, a comparison of the simulation andtest-beam results is described for dE/dx, transition radiation and drift-time measurements atdifferent counting rates (from 0 to 18 MHz).

Figure 3-70 Illustration of how ionised electrons drift to the anode wire in a TRT straw.


92 3 Simulation

3.7.3.1 dE/dx and Transition Radiation

To understand the electron identification ability of the TRT, careful calculations of the energydeposited by ionisation and transition radiation (TR) were introduced into the standard ATLASInner Detector simulation. The ability to identify electrons and reject hadrons is determined bythe relative amounts of TR and ionisation deposited in the straws. The TR performance on sin-gle tracks is presented in Section 4.6.

The actual ionisation (dE/dx) deposited in a hit straw is calculated from the track energy andpath length in the straw. Tables of precalculated energy depositions and ionisation productionare used to determine the expected number of electron clusters and their energies along theflight path of the track through the straw. The energy of the ionisation deposited in a straw iscalculated entirely during digitisation using the Lorentz γ factor of the track. The ionisation en-ergy deposited is calculated using the Photo Absorption Ionisation (PAI) Model [3-6][3-7] (theionisation calculated by GEANT is not used). Figure 3-71 shows a comparison between TRTtest-beam measurements and the PAI model of the differential dE/dx spectrum of chargedpions [3-9].

The situation is more complicated for TR photons, where it is necessary to make modificationsnot only at the digitisation phase, but also to modify GEANT to generate TR photons during thesimulation phase (standard GEANT does not). In the latter, TR photons are generated only in ma-terial which can produce TR photons and only for charged tracks with suitably large Lorentzfactors: βγ > 1000 (essentially only electrons). The emission of TR photons with appropriate en-ergy is simulated following the formulae of [3-10][3-11] and the simulation is tuned to test-beammeasurements of the relevant radiator materials (see Section 12.2.3). Once a TR photon is pro-duced, the possibility exists for it to be absorbed by dead material before even reaching the xe-non gas mixture inside the straw.

At digitisation, the energy of absorbed TR photons is added to the straw output signal.Figure 3-72 shows a comparison between TRT test-beam measurements and the simulation for30 GeV electrons. The differential spectrum of the deposited energy shows the same dE/dx

Figure 3-71 Ionisation energy deposition collected ona straw from pions with pT = 20 GeV.

Figure 3-72 Combined ionisation and TR energy dep-osition collected on a straw from electrons withpT = 30 GeV.

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3 Simulation 93

shape as seen for the pions, but with a significant tail at high energy coming from TR photons.Figures 3-71 and 3-72 demonstrate that the simulation accurately reproduces the details of thedifferential spectra for dE/dx (pions) and dE/dx combined with transition radiation (electrons).

3.7.3.2 Drift-time Measurements

The drift-time measurements described in Section 12.2 are compared here to the simulation us-ing the stiff muon dataset described in Section 3.7.5.2. The simulation model can thus be studiedto ensure that it reproduces the basic characteristics of the straw tubes and their associated elec-tronics. In all the plots shown, both the real electronics and the simulated signal shape used a7.5 ns peaking time. To approximate the test-beam geometry, only single muon hits with|η| < 0.35 in the barrel TRT layers were used in the simulation. The efficiencies given in thissection have been calculated based on the number of hits found within ±2.5σ of the nominaltrack position. The jitter of the cluster arrival-time was turned off for these comparisons in orderto match the measured test-beam spatial resolution. Electronic noise was not simulated for rea-sons of speed in the simulation.

Figure 3-73 shows the comparison1 of the measured resolution and the resolution generated bydigitising high-pT muons with no jitter factor. The comparison is shown as a function of the dis-criminator threshold setting with no background (corresponding to zero luminosity). The meas-ured data is taken from Figure 12-27. It can be seen that the simulated resolutions agree withthose measured in the test-beam.

Figure 3-74 shows a comparison of the efficiency for finding a hit within ±2.5σ of the corre-sponding track. The simulated efficiency is somewhat high because the residuals from the sim-ulation display less tails than the experimental data due to the absence of electronic noise. Thevariation of the efficiency as a function of threshold is in reasonable agreement with the meas-ured data.

1. The points labelled ‘Full GEANT simulation’ were obtained using the simulation of the full Inner Detec-tor and were not obtained using the stand-alone simulation shown in Section 12.2.2.2.

Figure 3-73 Spatial resolution as a function of dis-criminator threshold.

Figure 3-74 Efficiency for finding hits within ±2.5σ ofthe nominal position as a function of discriminatorthreshold.

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94 3 Simulation

Figure 3-75 shows good agreement for themeasured and simulated dependences of theresolution on the straw counting rate. Themeasured resolution shown in Figure 3-75 isthe data of Figure 12-30 compensated to ac-count for the difference between single-hit andmulti-hit TDC measurements in the test-beamdata. Figure 3-76 shows the dependence of thedrift-time efficiency on the straw countingrate. Although there is fairly good agreement,some discrepancy arises from the fact that inthe simulation, background is simulated cor-rectly as coming from minimum-ionising par-ticles, while on the other hand in the test beamthe background rate was mimicked by anX-ray source. Figure 3-77 shows the probabili-ty of recording a hit from an electron withpT = 30 GeV in a straw as a function of the dis-tance of the track to the straw centre1. It can beseen that the straw has a high efficiency acrossits radius, with a rapid fall and a small regionof reduced efficiency at the edge. The tail inthe distribution, corresponding to tracks notdirectly crossing the straw, is predominantlycaused by δ-ray electrons and to a lesser extentby electronic noise.

1. The simulation results shown in Figure 3-77 are derived from an earlier test-beam simulation [3-9] andnot from the current ATLAS simulation.

Figure 3-75 Spatial resolution as a function of rate. Figure 3-76 Efficiency for finding hits within ±2.5σ ofthe nominal position as a function of rate.

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3 Simulation 95

3.7.4 Simulation of Straw Response

3.7.4.1 Simulation Conditions for Drift-time Measurement, Rate and Occupancy Studies

To simulate the effect of non-zero luminosity, the hits of many minimum bias events are super-imposed (piled-up) and then digitised as a single overall event. The studies presented in thissection use a method of simulating pile-up which differs from the usual ATLAS method be-cause particle flight-time is used. The minimum bias events are assigned to beam-crossings be-fore, during, and after the beam-crossing of interest; the flight-time of the tracks to the TRT fromtheir time of generation is used, and only hits which are in-time with a reasonable gate are con-sidered (see Section 3.7.5.2). For the design luminosity of 1034 cm-2s-1, a Poisson mean of 23 min-imum bias events was used in each beam-crossing from four before (-4) to two after (+2) thecrossing of interest. The disadvantage of this pile-up method is that it requires large amounts ofcomputer time and memory to process the large number of minimum bias events needed. Withthe exception of the rate studies, which do not need a time cut or a gate, all studies in Section 3.7used events superimposed in this way.

Low energy tracks generated in an underlying event or in pile-up can loop through the TRT forover 100 ns and thus affect the readout of data from interactions in later beam-crossings. There-fore, to ensure no losses, hits were recorded for up to 256 ns during the simulation of an event.

The energy cutoff used in GEANT to determine if a track had stopped was lowered to 100 keVfor all particle types. When the energy of a track falls below this cutoff value and the track stopswithin the active volume of a straw, the PAI model described in Section 3.7.2 is used to distrib-ute the remaining track energy in the straw.

3.7.4.2 Drift-time Measurement Efficiency

To study the efficiency with which hits from ‘signal’ tracks are recorded, muons of pT = 10 GeVwere generated with all GEANT interactions turned off (except ionisation loss which is needed torecord hits). The distribution of the difference between the reconstructed and true drift-time forall layers combined is shown in Figure 3-78 for muons with no background. The tail of large re-sidual hits is associated with tracks that pass very close to the wire and generate hits with verylate drift-times. Figure 3-79 shows how the r.m.s. of this distribution varies as a function of |η|.The observed variation versus |η| is of the order of 10%. The drift-time measurement is subse-quently transformed into a spatial position, and the residuals of this are shown in Figure 3-82.Requiring that hits exceed a 200 eV threshold removes 4% of hits; requiring that the hits shouldlie within ± 2.5σ of the true position removes a further 4%.

Figure 3-80 shows for zero luminosity the efficiency for finding high-pT muon hits withinthe ± 2.5σ road (and above the threshold) as a function of |η|. The efficiency has some depend-ence on |η| because the amount of ionisation deposited in a straw depends on the path lengthof the track in the straw, which in turn is a function of |η|. The effect is most pronounced in thebarrel layers at higher |η| where tracks originating at the interaction point cross the layers at ashallow angle.

Figure 3-81 shows the muon drift-time efficiency as a function of the luminosity for the innerbarrel (most occupied), outer barrel (least occupied), middle short wheel, and middle longwheel layer. While the muon hits were generated using only ionisation, all interactions were en-


96 3 Simulation

abled for the background minimum bias events. Even at twice the design luminosity, the effi-ciency in the layers with the highest occupancies stays above 60%.

3.7.4.3 Spatial Resolution

Calculations of spatial resolution follow directly from the time difference distributions used forthe efficiency calculations in Section 3.7.4.2. The Rφ residuals are shown for single tracks in theabsence of pile-up in Figure 3-82. The actual resolution generated by the simulation is control-

Figure 3-78 Differences between reconstructed andtrue drift-time for pT = 10 GeV muons at zero luminos-ity.

Figure 3-79 Drift-time resolution for high-pT muonsas a function of |η| at 1034 cm-2s-1.

Figure 3-80 Efficiency for drift-time hits from high-pTmuons within a 2.5 σ window as a function of |η| atzero luminosity.

Figure 3-81 Efficiency for drift-time hits from high-pTmuons within a 2.5 σ window as a function of luminos-ity for the most and least occupied layers.

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3 Simulation 97

led by an ad hoc time jitter factor introduced in the TRT electronics response model. Without thejitter factor, the very detailed electronics model correctly reproduces the resolution measured ina test-beam using single straws, which is considerably better than the one expected in the actual4 × 105 channel TRT system, as explained in Section 3.7.2. At low luminosity averaged over alllayers, the resolution is 117 μm without and about 170 μm with the jitter. The resolution isshown as a function of luminosity in Figure 3-83. The resolution rises to about 200 μm in thehighest-rate layers at design luminosity.

3.7.5 Rates and Occupancies

The relevant quantities which characterise the straw operating conditions at high luminosityare:

• Rate - the rate at which charged particles cross a straw.

• Hit occupancy - the fraction of straws with hits (not necessarily drift-time hits).

Several of the plots which will appear in this section are ordered by increasing R in the barreland increasing |z| in the end-cap. There are four distinct regions (details can be found inSection 3.1.3):

• Short barrel: 56 ≤ R ≤ 62 cm.

• Full length barrel: 62 ≤ R ≤ 107 cm.

• Short wheels: 83 ≤ |z| ≤ 278 cm.

• Long wheels: 282 ≤ |z| ≤ 335 cm.

Figure 3-82 Residuals for pT = 10 GeV muons atzero luminosity.

Figure 3-83 Spatial resolution in the TRT as a func-tion of luminosity.

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98 3 Simulation

3.7.5.1 Total Charged Particle Rate

The total charged particle rate has direct bear-ing on the analogue electronics design andalso on how quickly the straw will age. Therate is simply the total number of charged par-ticles crossing a straw per second, and is es-sentially a geometrical acceptance calculation.

Figure 3-84 shows the rate of all particles andthe rate of all secondaries1 in the various TRTlayers at the design luminosity of 1034 cm-2s-1.The rates shown are adjusted to include an es-timate of the low energy particles (mainlyelectrons) from interactions of the neutronsand low-energy photons with the detector ma-terial and the expected LHC duty factor of80%. For each size of wheel, the average rateshows relatively small dependence on the zposition of the wheel, with a mean of 7 MHzin the short wheels and 18 MHz in the longwheels. For the full length barrel layers, therate varies drastically as a function of the radius of the layer: from 18 MHz (inner) to 5 MHz(outer). The short barrel layers vary from 10.4 MHz (inner) to 8.6 MHz (outer). The local ratesaveraged over a fill in the barrel and wheel layers (especially the longer wheels) vary considera-bly with radius, as is shown in Figures 3-85 and 3-86. Also, the maximum local rates are shown,corresponding to sampling over all beam-crossings (i.e. not including the effect of the LHC dutyfactor).

3.7.5.2 Straw Hit Occupancy

The straw hit occupancy depends on the time interval which is used to validate the hit. The TRTfront-end electronics reads out the straws during three consecutive time slices of 25 ns each. Ifthis wide time interval of 75 ns were used to validate a hit straw, the hits from many neighbour-ing bunches would be recorded as valid hits, and the effective straw hit occupancy would risedramatically. In order to reduce it significantly, the possibility to record the straws which havefired the low-level discriminator is foreseen in an optimised time interval (gate) in the TRTread-out electronics. The time intervals of interest are significantly smaller than the total drifttime, typically 10 to 15 ns.

This method, used to minimise the straw hit occupancy, is based on the fact that each particlecrossing the straw usually deposits energy near the straw wall (cathode). In principle, with theapplication of a narrow gate, positioned close to the maximum drift time of 42 ns, a high effi-ciency for recording hits from the trigger bunch can be achieved, while effectively suppressingthe hits from the neighbouring bunches, which have the same distribution but are shiftedby 25 ns. The efficiency for the in-time hit registration and the overall occupancy depend on the

1. Secondaries consist of all particles created by material interactions in GEANT. All hits caused by second-ary tracks with a kinetic energy above 100 keV are included in the secondary rates. Particles with energybelow 100 keV are stopped immediately by GEANT and their energy is deposited at that point.

Figure 3-84 Rates in the TRT as a function of layer at1034 cm-2s-1.

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position of this gate and its width. The gate must be wide enough to allow for hits from thein-time beam-crossing to be recorded with reasonable efficiency but not so wide that too manyhits from the out-of-time beam-crossings are accepted. For all results shown below the gate cho-sen was 12.5 ns.

The contributions of bunches from different beam-crossings (4 before to 2 after) to the occupan-cy of a given beam-crossing and averaged over all straws are shown in Table 3-16. The contribu-tions of all of these bunches and of just the in-time bunch are shown in Figure 3-87. The numberin Table 3-16 corresponding to bunch 0 is the straw hit occupancy averaged over the whole de-tector for the in-time bunch and therefore corresponds to the average of the dashed histogramin Figure 3-87. Table 3-16 shows that the additional occupancy from the neighbouring beamcrossings is almost entirely due to the previous (-1) and next (+1) beam crossings.

Figure 3-87 shows the straw hit occupancy for each layer in the TRT at design luminosity (upperpoints), using a 12.5 ns wide gate and including all the out-of-time bunches. At design luminos-ity, the occupancy of the full-length barrel layers ranges from 38% (inner) to 13% (outer); theshort barrel layers range from 26% (inner) to 22% (outer). The short wheels range from 15% to21%, and the longer wheels average about 35-36%. The occupancy from the in-time bunch onlyis also shown (bottom points). The contribution of the out-of-time beam-crossings is found to beabout 25-30% of the total straw hit occupancy. Figure 3-88 shows the dependence of the strawhit occupancy on the luminosity for the various types of straw layers.

Figure 3-85 Rates (per cm) in the TRT barrel as afunction of radius at 1034 cm-2s-1.

Figure 3-86 Rates (per cm) in the TRT long wheelsas a function of radius at 1034 cm-2s-1.

Table 3-16 Straw hit occupancy from different beam-crossings at the design luminosity of 1034 cm-2s-1 for agate width of 12.5 ns (see text). The straw hit occupancies from each beam-crossing are estimated as inde-pendent contributions, whereas the total occupancy includes the correlations between the different beam-cross-ings.

Beam-crossing −4 −3 −2 −1 0 +1 +2 All

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The standard procedure to produce pile-upwithin the ATLAS simulation framework (seeSection 2.6) is based on pile-up in a singlebeam-crossing with 32 pile-up events in thecase of the TRT instead of the 23 foreseen perbeam-crossing. This number was based onearlier studies, which had indicated that, witha narrow gate of the type described above, theeffective straw hit occupancy at design lumi-nosity was about 30% to 40% higher than thatdue to the in-time bunch. A study was under-taken to check that this procedure, usedthroughout the rest of this TDR, reproducesthe work described here. Figure 3-89 showsthe straw hit occupancy as presented inFigure 3-87 including all beam-crossings. Theresults obtained using the standard procedurewith an average of 32 in-time minimum biasevents are superimposed in Figure 3-89 andreproduce well the results of the more correctsimulation. More work is in progress to checkthe level of agreement between the two procedures for the drift-time measurements.

There is considerable event-to-event variation in the occupancy around its mean value andFigure 3-90 shows, as an example, this variation for the innermost barrel layer of long straws fordifferent luminosities from 5 × 1032 to 2 × 1034 cm-2s-1.

Figure 3-87 Straw hit occupancy in the TRT as afunction of layer at 1034 cm-2s-1.

Figure 3-88 Straw hit occupancy as a function ofluminosity.

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Figure 3-89 Straw hit occupancy using full simulationof time information from 7 beam-crossings each of 23minimum-bias events and using 32 in-time events.

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3.7.5.3 High-Threshold Hit Occupancy

As in the case of the straw hit occupancy forlow-threshold hits, the width of the gate usedto read out the high-threshold or transition ra-diation candidate hits has an influence on thehigh-threshold occupancy of the straws. Butfor the high-threshold hits, the TRT readoutscheme does not allow any special gate, otherthan the natural one defined by the 25 ns repe-tition rate.

Of course, far fewer hits reach the 5 keV highthreshold than the 200 eV low threshold. Inminimum bias background events, nearly allthe high-threshold hit occupancy is caused notby energetic electrons but by pions and otherhadrons producing large amounts ionisation.Two gates were used to calculate thehigh-threshold straw hit occupancy: a 25 ns (1beam-crossing) and a 50 ns (2 beam-crossing)gate. The 25 ns gate minimises occupancywith high efficiency and the 50 ns gate ensures full efficiency for recording transition radiation(TR) hits at the expense of increased high-threshold occupancy. The offset for both the 25 ns andthe 50 ns gates was chosen to maximise the efficiency for recording true TR hits generated by

Figure 3-90 Straw hit occupancy distribution for the inner layer of the full barrel for different luminosities.

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Figure 3-91 TR hit occupancy in the TRT as a func-tion of layer at 1034 cm-2s-1.

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100 GeV electrons. With the optimal offset, the 25 ns gate proved to be only 2% less efficientthan the 50 ns gate for signal hits from transition radiation. Figure 3-91 shows the high-thresh-old straw hit occupancy for each layer in the TRT at design luminosity, using the 50 ns widegate (upper points) and the 25 ns gate (lower points). The high-threshold occupancy never ex-ceeds 8.2% even when using a 50 ns gate in the highest rate layer. The 25 ns gate occupancy isabout 65% of that from the 50 ns gate, instead of ~50% which might be expected, because of thefinite width of the high-threshold pulses (15-20 ns) and of the spread of their arrival times.

3.7.5.4 Effect of Backsplash from Calorimeter

A study was undertaken using the standard ATLAS GEANT simulation to ascertain the level ofbacksplash from the calorimeter, solenoidal magnet and their cryostat. For most of the Inner De-tector studies, the calorimeter is not used when simulating events so as to reduce computer timefor this step. Using a small dataset of 300 minimum bias events, the rates in the TRT were com-pared for when the calorimeter was active in the simulation and when it was not. Although thestatistics were not great enough to get an absolute measure of the change in rate caused by thecalorimeter for each TRT layer, it was possible to estimate the relative increases. The average in-crease in the total number of hits in a layer was around 7.5%, while the largest increase in anylayer was less than 15%. Previous test-beam studies [3-12] also have shown this effect to besmall, although underestimated by GEANT in some cases.

3.8 References

3-1 ATLAS Collaboration, CERN/LHCC 93-24.

3-2 A. Poppleton, ATLAS Internal Note, INDET-NO-077.

3-3 ATLAS Collaboration, Technical Proposal, CERN/LHCC/94-43, LHCC/P2.

3-4 ATLAS Collaboration, Calorimeter Performance Technical Design Report,CERN/LHCC 96-40.


3-6 W. Allison and J. Cobb, Ann. Rev. Nucl. Part. Sci. 30 (1980) 253.

3-7 V. Grishin et al., Nucl. Instr. Methods A307 (1991) 273.

3-8 RD6 Collaboration, ATLAS Internal Note, INDET-NO-018.

3-9 W. Funk, ATLAS Internal Note, INDET-NO-157.

3-10 G. Garibyan, Sov. Phys. JETP 33 (1971) 23.

3-11 M. Cherry et al., Phys. Rev. 10 (1974) 3594.



4 Single Track Performance 103

4 Single Track Performance

In this chapter, the properties of single tracks are examined. A summary consisting of a parame-trisation of the track parameter errors is provided in Section 4.5. In considering single tracks,the properties deduced represent an idealisation of what can be expected in normal LHC oper-ating conditions. The properties examined depend on the detector resolutions and material de-scription described in the previous chapter, but do not depend significantly on patternrecognition. The effect of nearby tracks is to cause tracks to pick up spoilt or wrong hits, andwhile this does not tend to modify the Gaussian core of the pull distributions1, it adds tails. Theeffect of these tails can be such that the track can no longer be considered to be well reconstruct-ed. This is examined more in the next chapter.

Frequently muons are used for studies of track parameter resolutions since they only incur ion-isation losses and multiple scattering, in the majority of cases. Hadrons, in particular pions, suf-fer from hadronic interactions in addition. The effect of these interactions can be to stop theincident track, so that it may prove impossible to reconstruct the track all together. However, if ahadron avoids interaction, the distribution of its reconstructed parameters is similar to thosefrom a muon. Things are quite different for electrons which are prone to emit bremsstrahlungwhile continuing with significantly reduced momentum. It is possible to improve the electronmeasurement by resorting to kink finding in the Inner Detector at lower pT and by using the cal-orimeter position measurement at higher pT - this is discussed in more detail in Section 6.1.

For the studies which follow, good agreement has been found between the different pattern rec-ognition programs (iPatRec, PixlRec, xKalman) and so in many cases, representative curvesfrom one of the programs are shown.

Analytic CalculationIn what follows, it has proved very helpful to compare the results obtained from the full ATLASsimulation DICE with an analytic calculation. This calculation has the following features:

• All subdetectors are modelled as continuous surfaces in a cylindrical geometry. The TRTwas simulated as a set of barrels extending to |z| = 2.8 m, complemented by end-capwheels out to |z| = 3.35 m.

• Uniform detector resolutions have been used. Where possible, these have been takenfrom test-beam data (to which DICE was tuned). However, it is important to allow for theη-dependence of the pixel resolution, hence this is parametrised along the lines of the re-sults of Section 3.5.4. The values used incorporate a small degradation to allow for detec-tor inefficiency.

• Material is represented in a simplified form to reproduce the main features of the modelused in DICE, and local inhomogeneities are ignored.

• Either the uniform or non-uniform magnetic field can be considered.

• The variation in z of the collision point is considered.

• Covariance matrices for track fits are analytically calculated and include multiple scatter-ing.

1. The pull is defined here as the difference between the reconstructed and generated parameter, normal-ised by the error on the reconstructed parameter.


104 4 Single Track Performance

As can be seen in the plots which follow, this calculation provides a good description of the re-sults from DICE. This provides confidence that the resolutions found in Chapter 3 are beingused correctly in the reconstruction and that the material distributions are as intended.

4.1 Momentum Resolution

Most often the quantities of relevance to the physics of hadron collisions are the pT and η oftracks since they characterise the production process. A detector with a solenoidal field essen-tially measures the sagitta and hence curvature of charged particles and so the quantity meas-ured with Gaussian errors is 1/pT. In the absence of interactions with material, for a fixed set ofmeasurement points, the error on 1/pT is independent of pT.

4.1.1 Basic Measurements

In Figures 4-1, 4-3 and 4-5, the pT resolutions for pT = 200, 2 and 1 GeV are shown without abeam constraint. In Figures 4-2, 4-4 and 4-6, the corresponding ratios of the pT resolutions withand without a beam constraint of σx = σy = 15 μm are shown. The points are obtained fromDICE, while the curves come from the analytic calculation, using a uniform B field. The compar-ison demonstrates that the complicated simulation of DICE reproduces the results obtainedmore simply and allows a cross-check of the description of subdetector layers and the materialdistribution. The effect of the beam constraint is fairly small due to the proximity of the B-layerwith its superior resolution in Rφ and the large number of measurements made at low radius.

At high pT, the resolution of the detector is fairly uniform up to |η| ≤ 1.9, since the Inner Detec-tor is designed to provide the same number of precision and straw hits for all η and at compara-ble radii. Beyond |η| = 1.9, although the number of hits is preserved, the reduced radial extentRmax available for tracking causes the resolution to behave like R2

max.

Figure 4-1 pT resolution for pT = 200 GeV, withoutbeam constraint.

Figure 4-2 Ratio of pT resolution with and withoutbeam constraint for pT = 200 GeV.

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At low pT, the resolution is dominated by multiple scattering and is related to the square-root ofthe number of radiation lengths in the complete active volume of the detector and slowly vary-ing angular terms. The pT resolution at pT = 20 GeV is somewhere between the two extremes.

Figure 4-3 pT resolution for pT = 20 GeV, withoutbeam constraint.


Figure 4-5 pT resolution for pT = 1 GeV, without beamconstraint.


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4.1.2 Effect of Solenoidal Field

The effect of a non-uniform magnetic field isshown in Figure 4-7. The effects are most sig-nificant at high |η|, as expected from thefringing of the field maps shown inSection 3.2. The effect is most important forhigh-pT tracks - the results for pT = 500 GeVare shown. It is less significant for low-pTtracks since the multiple-scattering reducesthe effectiveness of measurements at large ra-dius and limits the overall resolution.

4.1.3 Sensitivity and Robustness

Figure 4-8 shows the effect of changing the resolution of various subdetectors. A beam con-straint is not used, since it tends to obscure the effect of degrading the pixels. It is clear that thegreatest sensitivity comes from the measurements at high radius, and for most of the accept-ance, the TRT dominates the resolution.

Figure 4-9 shows the effect of completely removing individual subdetectors from the Inner De-tector. Again the most severe degradation is associated with removing the TRT measurements.For |η| < ~2.2, the TRT dominates the resolution; however for larger |η|, the precision layersare essential to maintain acceptable resolution up to |η| = 2.5 (σ(1/pT) < 1 TeV-1 - see specifica-tion B3) because of the reduced radius of the TRT measurements and the reduction in Bz. FromFigure 4-8 it can be seen that the sensitivities to the pixels and SCT are about the same in the ab-sence of a beam constraint. However, with the beam constraint, the sensitivity to the pixels isgreatly reduced, as shown in Figure 4-9.

Figure 4-7 pT resolution from analytic calculation forhigh-pT tracks with uniform 2 T field and with solenoi-dal field. A beam constraint is used.

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4.1.4 Effect of Pile-up

The principle effect of pile-up on hit resolutionis to degrade the performance of the TRT, asshown in Section 3.7.4. Hits from pile-uptracks shadow some fraction of the hits fromsignal tracks, resulting in inefficiencies and atthe same time degrading the spatial resolu-tion. By contrast, the high granularity (low oc-cupancy) and low noise of the silicon detectorsmeans that their resolution is hardly affected.Figure 4-10 shows the comparison between pTresolution for high-pT tracks1 without anypile-up and with pile-up at 1034 cm-2s-1.

1. Although this is shown for pT = 500 GeV, since at high-pT the resolution is entirely dominated by meas-urement errors, the resolution in 1/pT should be identical to that at pT = 200 GeV.

Figure 4-8 pT resolution from analytical calculation(|η| < 2) for high-pT tracks showing the sensitivity tovarying resolutions of different subdetectors withinInner Detector.

Figure 4-9 pT resolution from analytical calculationfor high-pT tracks showing the effect of removing com-plete subdetectors. A beam constraint is used as isthe real B-field.

0.8

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Figure 4-10 pT resolution for pT=500 GeV, withoutand with pile-up at 1034 cm-2s-1. A beam constraint isused.

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4.2 Charge Determination

The intention of the specification B3 (pTσ(1/pT) < 0.3 for pT = 500 GeV) is to ensure good chargesign measurement at very high pT. The is important for signatures of physics beyond the stand-ard model such as searches for leptonic decays of heavy gauge bosons, W′ or Z′. Whereas highenergy muons will be more accurately measured by the Muon Spectrometer, the sign of thecharge of high-pT electrons can be measured only by the Inner Detector, while their energy isprecisely measured by the EM calorimeter.

High-pT electrons and muons have been re-constructed with xKalman. Figure 4-11 showsthe 1/pT distribution of 1000 GeV muons andelectrons with a beam constraint on the trackfit. The distribution of pulls in 1/pT is Gaus-sian and the fraction of wrong sign tracks is2.0 ± 0.1%, which agrees with the fraction pre-dicted from the Gaussian errors of the track fit.The beam constraint is particularly importantfor |η| > 2, where the effective radius oftracking is reduced. The non-uniformity of themagnetic field has been taken into account bysmearing the distributions obtained by the fullsimulation to reproduce the Gaussian resolu-tion observed in Section 4.1.2 (which was de-termined using the analytical calculationdescribed at the start of this chapter).

From Figure 4-11, it is clear that the distribu-tion for electrons has large tails. Hard bremsst-rahlung tends to increase the absolutecurvature, giving a large tail towards low pT. However, it is the tail at high pT which contributesto the wrong sign tracks. This tail comes from electrons where a hard bremsstrahlung photonconverts almost immediately into a high-pT e+e− pair. For example, 19% (8%) of electrons withpT = 1000 GeV will produce at least one secondary electron with a pT > 10 GeV (100 GeV) beforeentering the TRT active region. Usually taking the highest-pT track (without the beam con-straint, which tends to increase significantly the pT of secondaries) is sufficient to pick the pri-mary electron, unless it has lost too much energy. Furthermore, sometimes the secondaryelectrons are so close that they spoil the hit reconstruction and the pattern recognition, resultingin reconstructed tracks with very high pT. To reduce these ambiguities, a cut on the fit χ2 wasmade.

The precise measurement of an electron’s transverse energy ET in the calorimeter will enable across-check with the pT measured in the Inner Detector. Approximating the calorimeter meas-urement by the true electron energy, the following additional cuts have been applied to elec-trons:

• Fit χ2 per degree of freedom < 1.

• pT > 100 GeV, for ET ≥ 500 GeV - to avoid low energy secondaries.

• pT < 10 ET - to avoid spoilt tracks.

Figure 4-11 pT distribution of electrons and muonswith pT = 1000 GeV over full η range; inset shows thesame histograms with a linear scale.

10-4

10-3

10-2

10-1

1

-0.01 -0.005 0 0.005 0.01

1/pT (GeV-1)

e-

μ-



The efficiency of these cuts is 92%, independ-ent of pT. The cuts reduce the wrong sign frac-tion from 6.2% to 4.4% for electrons withpT = 1000 GeV.

Figure 4-12 shows the wrong sign fraction forpT = 1000 GeV electrons as a function of |η|,along with the values which would be expect-ed from a Gaussian distribution with the nom-inal resolution. The Gaussian part dominatesfor |η| > 2 due to the reduced effective radiusand the non-uniform magnetic field. Materialeffects dominate at lower |η|, in particularfor 0.8 < |η| < 2.0. The shape of the curve fortrack selection inefficiency also reflects the dis-tribution of material in the Inner Detector.

The wrong sign fractions for muons and elec-trons with different pT are shown in Table 4-1.The tails for muons are dominated by thenominal resolution of the Inner Detector,while this is only true for electrons at veryhigh pT, greater than ~1.5 TeV.

At the LHC design luminosity of 1034 cm-2s-1, pile-up events tend to degrade slightly the mo-mentum resolution (as seen in Section 4.1.4) and make pattern recognition more difficult. How-ever, no increase of the wrong sign fraction is seen for pT = 500 GeV. The only change observedis a loss of efficiency of < 3%.

a. Numbers in brackets are what would be expected from a Gaussian distribution with the nominal reso-lution.

Table 4-1 Wrong sign fraction for high-pT muons and electrons.

pT (GeV) Wrong sign fraction (%)

Uniform B fielda Real B field

Muons Electrons Muons Electrons

500 0.04 (0.02) 1.2 (0.03) 0.2 1.4

1000 0.9 (0.9) 3.6 (1.2) 1.9 4.4

2000 9.2 (9.1) 11.5 (10.1) 11.6 13.3

Figure 4-12 Wrong sign fraction as a function of |η|for pT = 1000 GeV electrons (circles). The histogramcorresponds to the part expected from the Gaussianerror. The dotted histogram and circles correspond toa uniform B field. The curve shows the inefficiencyafter the electron cuts.

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Inefficiency

WS AllWS Expected

|η|



The evolution with pT of the wrong sign frac-tion for muons and electrons is shownFigure 4-13. The absolute difference betweenelectrons and muons decreases slightly for pTgreater than ~1 TeV, since the electrons actual-ly benefit from soft bremsstrahlung reducingtheir momenta. The efficiency is found to beindependent of pT.

This study demonstrates that in the range ofinterest for W′ and Z′ searches (pT < ~2 TeV),the Inner Detector can measure muon andelectron charge asymmetries without majordistortions.

4.3 Angular Resolution

The resolutions for φ and cotθ are shown in Figures 4-14 to 4-17. As for the 1/pT resolution, theφ resolution is fairly constant with |η| at high pT due to the provision of sets of Rφ measure-ments at approximately the same radii for all η. The resolution for cotθ is constant in the preci-sion barrel region (|η| ≤ ~1.0), but since the precision end-caps measure R, the resolution riseslike cotθ. The angular resolution in the R-z projection is σ(θ) = sin2θ σ(cotθ). It can be seen thatat high pT, this is significantly better than the 2 mrad proposed in the specification (B4). Atη = 0, 103 × σ(cotθ) = 0.70; this rises to a) 1.10 with just pixels, b) 3.45 with just SCT and c) 1.21with the B-layer and the last SCT layer. Therefore the source of the good resolution is a combi-nation of the lever arm of the pixels, the level arm of the precision tracker and the effective σzmeasurement of the SCT which results from the choice of the stereo angle.

Figure 4-14 φ resolution for pT = 200 and 20 GeV. Figure 4-15 φ resolution for pT = 1 GeV.

Figure 4-13 Wrong sign fraction as a function of pTfor muons and electrons.

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4.4 Impact Parameter Resolution

Impact parameter measurements are essential for:

• Secondary vertex reconstruction: e.g. B decays, V0 decays.

• Heavy-flavour tagging.

• Lifetime measurements.

• Associating tracks to the correct primary vertex at high luminosity.

At high momenta (pT > ~20 GeV), the resolution is determined by measurement precision andis dominated by the first layer, namely the B-layer at R = 4 cm. Nevertheless, the TRT does con-tribute through the measurement of track curvature and improves the resolution by about 20%.

Since the measurement of impact parameter is dominated by the first few layers, a great dealcan be learnt from a simple two layer model. Given a first measurement layer with resolution σ1at R = R1 and second with σ2 at R = R2, the impact parameter resolution for a track at normal in-cidence is

where α1 is a the constant related to the multiple scattering angle at the first plane. Additionalsimple angular factors (different for barrel and disk geometries) can be included to describe thetransverse and longitudinal impact parameters (d0 and z0, respectively) as a function of atrack’s direction. This formula leads to the simple parametrisation A ⊕ B/pT, where A and Bcan be considered to be functions of |η|. This parametrisation is only approximate [4-1], butnevertheless, quite useful and will be presented explicitly in Section 4.5.

The B-layer is explicitly designed so that charge is spread over several pixel cells. Since the im-pact parameter is very sensitive to the resolution in this layer, it depends on the way in whichclusters are formed and how the coordinate is estimated. This is done in a slightly different

Figure 4-16 cotθ resolution for pT = 200 and 20 GeV. Figure 4-17 cotθ resolution for pT = 1 GeV.

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R1σ2 R2σ1⊕R2 R1–

----------------------------------α1R1

pT-------------⊕



manner for the three pattern recognition algorithms which have been used, and leads to slightlydifferent estimates for the resolution. This is illustrated for high-pT in Figure 4-18 and 4-19. Atlow-pT, there are no significant differences, since the resolution is dominated by multiple scat-tering in the first layer. Further, the differences are less than the uncertainties coming from thepixel resolution.

4.4.1 Impact Parameter as a Function of pT and |η|

In this section, the resolutions from just one of the algorithms (iPatRec) are shown, with andwithout the B-layer. In the studies ‘without the B-layer’, the material of the B-layer was kept inthe simulation, but its measurements were not used. Compared with the complete removal ofthe B-layer, this situation is slightly pessimistic at low pT (at η = 0, for pT = 1 GeV, σ(d0) increas-es by 10 μm) but there is no difference at high pT.

The transverse impact parameter resolution σ(d0) is shown in Figures 4-20 and 4-21. Since theresolution at high pT depends on the measurement error and is dominated by the B-layer, theresolution is fairly constant as a function of |η|, with some improvement due to the increasedcluster size at larger |η|.

The longitudinal impact parameter resolution σ(z0) is shown in Figures 4-22 and 4-23. This ismanifestly worse than in the transverse direction due to the poorer z resolution of the B-layer.However, the improvement due to the increased cluster sizes at larger |η| is even moremarked.

For lifetime related measurements, it is more interesting to consider the projection of the impactparameters on to a plane transverse to the track direction. Hence it is better to plot σ(z0) multi-plied by cosλ = sinθ. This is shown in Figures 4-24 and 4-25. It is to be expected that at low pT,where multiple scattering dominates, the resolution in the two projections should become thesame. This is not seen here since the equality only becomes apparent for pT much less than can

Figure 4-18 Comparison between transverse impactparameter resolutions for different pattern recognitionalgorithms.

Figure 4-19 Comparison between longitudinal impactparameter resolutions for different pattern recognitionalgorithms.

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be measured by the Inner Detector1, and even then there is a small difference because σ(d0) isobtained from a 3 parameter fit, whereas σ(z0) comes from a 2 parameter fit [4-1].

The impact parameters of pions with pT = 1, 5, 20 and 200 GeV have been examined. While thedistributions of the differences between the reconstructed and generated parameters tend tohave large tails due to interactions, the resolution derived from the cores of the distributionsgive resolutions which agree with those from muons to better than 5%.

1. At pT = 1 GeV, σ(z0) is not completely dominated by multiple scattering at η = 0.

Figure 4-20 Transverse impact parameter resolutionfor pT = 200 GeV.

Figure 4-21 Transverse impact parameter resolutionfor pT = 1 GeV.

Figure 4-22 Longitudinal impact parameter resolutionfor pT = 200 GeV.

Figure 4-23 Longitudinal impact parameter resolutionfor pT = 1 GeV.

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The impact parameters are shown as a function of pT for |η|~0 in Figures 4-26 and 4-27. Thecurves correspond to the parametrisation A ⊕ B/pT, where A has been determined from the im-pact parameter at high-pT and B from pT = 1 GeV. With the B-layer, the multiple-scattering termis dominated by the scattering at the B-layer, giving B a behaviour like 1/√sinθ for d0 and like1/√sin3θ for z0.

Figure 4-24 Longitudinal impact parameter resolutionprojected on to the transverse plane for pT = 200 GeV.

Figure 4-25 Longitudinal impact parameter resolutionprojected on to the transverse plane for pT = 1 GeV.

Figure 4-26 Transverse impact parameter resolutionas a function of pT for |η| ≈ 0. Curves are analytic fits.

Figure 4-27 Longitudinal impact parameter resolutionas a function of pT for |η| ≈ 0. Curves are analytic fits.

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4.5 Summary of Parameter Resolutions

In the approximation that multiple scattering can be described as angular deflections with aGaussian distribution, the error matrix for the helix parameters resulting from a simple χ2 fit tothe measurements in the Inner Detector has the form in matrix notation: (DT(M0+Ms)-1D)-1

where the D’s are Jacobean’s (relating coordinates to helix parameters), M0 represents the errormatrix for the intrinsic measurements and Ms represents the error matrix for the multiple scat-tering, with Ms ∝ pT

-2. Consequently, the parameter error matrix has an approximate formA ⊕ B/pT - this approximation is generally not too bad, although only correct in the asymptoticlimits of pT → 0 or ∞ [4-1].

Using the analytic calculation described at the start of this chapter (which has been shown toprovide a good approximation to the full simulation of the Inner Detector), parametrisationshave been obtained (with the B-layer, without a beam constraint and with a uniform 2T field)for the track errors: σ(p) = Aσ ⊕ Bσ/pT and the correlation coefficients ρ(p,q) = Aρ

2 + Bρ2/pT

2,where p and q are helix parameters. Angular factors have been absorbed in the coefficients Aand B. These coefficients have been determined from examining the error matrix for pT = 1 GeVand pT = ∞ and are presented in Tables 4-2 and 4-3. The ratios Bσ/Aσ give the momenta atwhich the intrinsic resolution and multiple scattering contributions are equal and presented inTable 4-4.

The correlation coefficients in Table 4-3 have been cross-checked with those from the full simu-lation and agree very well. The numbers contained in these tables will be encapsulated in a sub-routine for use in parametric studies with fast simulation.



Table 4-2 Coefficients describing helix parameter errors.

|η| 1/pT (TeV-1) φ (mrad) d0 (μm) cot θ ×103 z0sinθ (μm)

Aσ

0.00-0.25 0.365 0.076 10.9 0.66 81.9

0.25-0.50 0.364 0.076 10.9 0.62 69.7

0.50-0.75 0.377 0.078 10.9 0.60 59.1

0.75-1.00 0.384 0.079 11.0 0.59 49.8

1.00-1.25 0.377 0.077 10.5 0.61 42.3

1.25-1.50 0.403 0.080 10.2 0.72 38.0

1.50-1.75 0.402 0.076 9.9 0.87 33.6

1.75-2.00 0.351 0.070 9.6 1.12 29.4

2.00-2.25 0.445 0.081 10.2 1.54 25.6

2.25-2.50 0.600 0.097 9.6 1.98 22.3

Bσ (GeV)

0.00-0.25 12.3 1.51 57.2 1.62 85.7

0.25-0.50 12.7 1.56 59.0 1.71 78.1

0.50-0.75 13.6 1.66 62.6 1.98 75.5

0.75-1.00 16.0 1.83 68.3 2.47 76.2

1.00-1.25 17.3 2.02 75.0 3.26 79.1

1.25-1.50 18.8 2.25 83.4 4.46 83.7

1.50-1.75 19.4 2.51 93.2 6.27 91.7

1.75-2.00 18.8 2.81 104.6 9.06 103.6

2.00-2.25 17.6 3.17 118.6 13.32 119.1

2.25-2.50 18.0 3.62 135.5 19.42 135.8

Table 4-3 Coefficients describing helix parameter correlations.

|η| (1/pT,φ) (1/pT,d0) (φ,d0) (cot θ,z0)

Aρ2

0.00-0.25 +0.93 −0.65 −0.82 −0.85

Bρ2 (GeV2)

0.00-0.25 +0.37 −0.29 −0.97 −0.84



4.6 TR Performance

One of the key performance requirements of the TRT is to contribute to the electron identifica-tion using the transition radiation (TR) signature. This enhanced identification is necessary inorder to identify a clean sample of inclusive high-pT isolated electrons in the LHC environment(see Section 6.1). It is also crucial for the extraction of the signal from J/ψ → e+e− decays (seeSection 6.2.1) as well as the identification of soft electrons in b-quark jets (see Section 6.2.2) andthe reconstruction of photon conversions (see Section 6.3.2).

The electron identification performance of any TR detector depends critically on the quality ofthe radiator and the effective length of detector (radiator and X-ray absorber) traversed [4-2]. Italso depends on the particle energy, since the TR production for electrons rises rapidly for ener-gies above 0.5 GeV and reaches saturation for most detectors around 2 GeV; whereas the proba-bility for charged pions to produce high-energy δ-rays in the straw gas also rises substantiallyas the pion energy increases from a few GeV to about 100 GeV [4-4][4-5]. The barrel TRT radia-tor is made of polypropylene/polyethylene fibres, which are expected to provide a TR yieldclose to 80% of that of a perfectly regular foil radiator; the end-cap TRT radiator is made of poly-propylene foils, which are expected to provide a TR yield close to 90% of the optimum. Resultsare shown for 2 ≤ pT ≤ 20 GeV, which is representative of the spectrum of interest. The detectorresponse to TR was tuned according to the predictions derived from a detailed comparison [4-3]with test-beam results and extrapolation to the ATLAS detector.

The simulated electron and pion samples were subjected to selection cuts emulating the triggerselection during data-taking. The resulting average electron efficiency for pT = 20 GeV was 86%,as expected after Level-2. The TR performance was evaluated from this sample of reconstructedtracks.

Table 4-4 Transverse momenta (Bσ/Aσ) at which the intrinsic resolution and multiple scattering contributions areequal.

|η| 1/pT φ d0 cot θ z0

Bσ/Aσ (GeV)

0.00-0.25 33.6 19.9 5.3 2.5 1.0

0.25-0.50 34.9 20.6 5.4 2.8 1.1

0.50-0.75 36.0 21.4 5.7 3.3 1.3

0.75-1.00 41.5 23.3 6.2 4.2 1.5

1.00-1.25 46.0 26.1 7.2 5.3 1.9

1.25-1.50 46.7 28.2 8.2 6.2 2.2

1.50-1.75 48.4 32.9 9.4 7.2 2.7

1.75-2.00 53.5 39.9 10.9 8.1 3.5

2.00-2.25 39.7 39.1 11.7 8.7 4.7

2.25-2.50 29.9 37.3 14.1 9.8 6.1



The distributions of hits above the TR threshold (TR hits) along the reconstructed electron andpion tracks are plotted in Figures 4-28 to 4-31 for pT = 2 and 20 GeV and for two selectedη regions. The 0 < |η| < 0.8 region corresponds to the barrel radiator while 1.6 < |η| < 2.2 cor-responds to the end-cap radiator. These figures display three effects:

• A large increase in the number of TR hits for electrons in the end-cap TRT with respect tothe barrel TRT. This is due to the better radiator in the end-cap TRT (see above) and to thelarger number of crossed straws in the chosen end-cap η range (see Section 3.3).

• A significant energy dependence of the high-threshold hit probability for pions due to therelativistic rise in the dE/dx, which is very large for Xe-mixtures. This effect can be seenboth for pions in the barrel TRT for which pT increases from 2 to 10 GeV, and for pions ofpT = 20 GeV in going from the barrel to the end-cap region.

• A small residual increase of the number of TR hits for electrons as a function of energy atfixed η, even though the number of TR hits is expected to saturate for γ ≈ 5000, i.e. forelectron energies of 2 to 3 GeV.

The pion rejection is determined by the size of the regions of overlap in Figures 4-28 to 4-31. Thepion efficiency as a function of the electron efficiency is plotted in Figures 4-32 and 4-33 forpT = 2 and 20 GeV respectively for the two rapidity regions considered above.

Figure 4-28 Number of TR hits for electrons andpions with pT = 2 GeV and 0 < |η| < 0.8.

Figure 4-29 Number of TR hits for electrons andpions with pT = 2 GeV and 1.6 < |η| < 2.2.

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The resulting pion rejection (the reciprocal of the efficiency) for a chosen electron efficiency of90% is shown in Figure 4-34 as a function of η for both pT = 2 and 20 GeV.

Due to the relativistic rise in the dE/dx losses, the potential rejection is, as expected, slightlybetter for pT = 2 than for 20 GeV, especially in the end-cap region. In the absence of pile-up, re-jection factors of 15 to 1000 can be achieved, depending on the momentum and rapidity. Forslightly lower electron efficiencies (~85%), the rejection which can be achieved would improveby a factor of ~2.

Figure 4-30 Number of TR hits for electrons andpions with pT = 20 GeV and 0 < |η| < 0.8.

Figure 4-31 Number of TR hits for electrons andpions with pT = 20 GeV and 1.6 < |η| < 2.2.

Figure 4-32 Pion efficiency as a function of electronefficiency for pT = 2 GeV.

Figure 4-33 Pion efficiency as a function of electronefficiency for pT = 20 GeV.

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4.6.1 Effect of Pile-up

In the presence of the pile-up at the design luminosity 1034 cm-2s-1, the expected occupancy forTR hits is between 2 and 5% depending on the straw position in the TRT detector (seeSection 3.7.5.3). Therefore, the average number of TR hits per reconstructed track increases by0.6 (0.8) for pions and by 0.9 (1.1) for electrons in the barrel (end-cap) region. The electrons see aslightly larger increase since they have more hits close to the high threshold which are pushedover by additional energy deposited by pile-up tracks. The resulting degradation of the elec-tron/pion separation is shown in Figure 4-33 for the chosen barrel and end-cap η ranges atpT = 20 GeV and in Figure 4-35 as a function of |η| also for pT = 20 GeV. The loss of rejectionranges from a factor of ~2 in the barrel TRT to a factor of ~5 in the end-cap TRT, resulting in re-jections of ~6 to ~60 at the design luminosity. As can be seen from Figure 4-33, the low luminos-ity rejection can be recovered in the barrel at high luminosity at the expense of a further 5% lossof the electron signal.

4.7 References


4-2 B. Dolgoshein, Nucl. Instrum. Methods A326 (1993) 434.


4-4 W. Allison and J. Cobb, Ann. Rev. Nucl. Part. Sci. 30 (1980) 253.

4-5 V. Ermilova et al., Nucl. Instrum. Methods 145 (1977) 555.

Figure 4-34 Pion efficiency as a function of |η| forfixed electron efficiency of 90%.

Figure 4-35 Pion efficiency as a function of |η| forfixed electron efficiency of 90% at pT = 20 GeV.

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5 Pattern Recognition 121

5 Pattern Recognition

In this chapter, detailed comparisons are made between the two pattern recognition algorithms,iPatRec and xKalman. The algorithms are described in Section 2.5.2 and are used extensivelyfor the results presented in Chapter 6.

5.1 Isolated Tracks

Excellent pattern recognition for isolated high-pT tracks, especially in the presence of pile-up, isessential for many physics topics, such as H → l+l−l+l−.

5.1.1 Efficiencies

5.1.1.1 Definition of Efficiency

The efficiency for track finding is determined from the study of single tracks in the absence orpresence of pile-up. Pattern recognition is performed by iPatRec in a ‘cone’ of Δη = ±0.1,Δφ = ±0.1 around the direction of the signal track obtained from the Monte Carlo KINE truth in-formation. However, xKalman performs track finding in the complete event, except in the pres-ence of pile-up where a similar cone is used to save computing time.

Efficiency is defined as the fraction of accepted reconstructed tracks. A reconstructed track is ac-cepted if it has

1. Number of precision hits ≥ 9 (out of a maximum of 11, ignoring overlaps).

2. Number of pixel hits ≥ 2 (out of a maximum of 3, ignoring overlaps).

3. At least one associated hit in the B-layer.

4. |d0| < 1 mm.

These cuts correspond to those which have been developed in the context of b-tagging, the con-sequences of which will be considered in Section 5.2. In addition, to validate the track, a loosematch with the KINE track was made by requiring that the original track contributed to the ma-jority of the hits in the reconstructed track.


Figures 5-1 and 5-2 show the efficiencies for finding muons in the absence of pile-up as a func-tion of |η| for different pT. It is clear that there is no significant loss of tracks at any |η| or atany momenta down to 1 GeV. The relatively lower efficiency from xKalman at low pT disap-pears if looser requirements on the number of precision hits are made - this will be investigatedmore in the future.

Figures 5-3 and 5-4 show the efficiencies for finding pions in the absence of pile-up as a functionof |η| for different pT. For pT = 1 GeV and 5 GeV there are clear losses of tracks, especiallyaround |η| = 1.6. This is entirely consistent with the loss of pions due to material interactionsin the Inner Detector (see Section 3.4.2.2), to which xKalman is intrinsically more sensitive be-


122 5 Pattern Recognition

cause it requires a continuous track from the TRT inwards. For pT = 200 GeV, the effect is greatlyreduced because high energy interactions inevitably result in a high momentum secondarywhose track parameters are compatible with those of the primary. The efficiencies averagedover |η| are summarised in Table 5-1.

Figures 5-5 and 5-6 show the efficiencies for finding pions with pile-up as a function of |η|.Even in the presence of pile-up at the design luminosity, there is no difficulty in finding thetracks, and the reduction in efficiency is small.

Figure 5-1 Efficiency for finding muons of various pTas a function of |η| (iPatRec).

Figure 5-2 Efficiency for finding muons of various pTas a function of |η| (xKalman).

Figure 5-3 Efficiency for finding pions of various pT asa function of |η| (iPatRec).

Figure 5-4 Efficiency for finding pions of various pT asa function of |η| (xKalman).

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Table 5-1 Efficiencies for finding muons and pions in the absence of pile-up, averaged over |η|. Numbers inbrackets are for events with pile-up.

pT (GeV) Muon efficiency (%) Pion efficiency (%)

iPatRec xKalman iPatRec xKalman

200 99.2 98.7 94.8 95.0

20 99.2 (99.1) 98.5 (97.6)

5 99.0 97.9 93.0 (93.2) 89.5 (88.6)

1 98.5 96.5 90.3 84.1

Figure 5-5 Efficiency for finding isolated pions withpT = 5 GeV as a function of |η| (iPatRec) with andwithout pile-up.

Figure 5-6 Efficiency for finding isolated pions withpT = 5 GeV as a function of |η| (xKalman) with andwithout pile-up.

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5.1.2 Tails of Distributions

In the previous section, it was seen that thereis a very high efficiency to ‘find’ tracks in theInner Detector. However, not only is it impor-tant to find tracks, but they must be well re-constructed. For high-pT muons, there is noproblem in finding the tracks and reconstruct-ing their parameters. Figure 5-7 shows thepull1 distributions for 1/pT for muons withpT = 20 GeV at zero and design luminosity, re-constructed with iPatRec. Although there isa slight degradation of the r.m.s. of the pulls ingoing to 1034 cm-2s-1, it is clear that there arefew events in the tails.

The measurement of the quality of the recon-struction will depend on the physics analysisundertaken. This could be examined by study-ing the ‘efficiency’ after some suitable cuts toremove tracks whose helix parameters havebeen poorly reconstructed. Instead the com-plementary study has been performed tostudy the fraction of tracks in the tails of thepulls of the distributions of 1/pT and d0. The tails for 1/pT have already been examined in thecontext of charge misidentification in Section 4.2. The tails in the distribution of d0 containtracks which limit the rejection of non-b jets (see Section 6.7). The tail fraction in theimpact parameter distribution is defined as the fraction of tracks where|d0(reconstructed)-d0(generated)| > 3σ(d0), with an equivalent definition for 1/pT. The resolu-tions used, σ(d0) and σ(1/pT), are those obtained from fitting Gaussians to the cores of the dis-tributions in different |η| intervals. The results which follow are determined at zeroluminosity.

5.1.2.1 Muons

Figures 5-8 and 5-9 show the tail fractions for pT = 1 GeV muons. The fractions are significantlygreater than would be expected for a perfect Gaussian distribution (0.27%). The fractions areslightly lower for iPatRec than for xKalman because of the loose χ2 cuts used in the trackfinding. The non-Gaussian tails are due dominantly to the non-Gaussian tails in multiple scat-tering and the fact that local variations in the amount of material traversed is not taken into ac-count in the track fits, but instead the averaged material associated with a superlayer is used.This causes the errors for some tracks to be underestimated. The magnitude of the non-Gaus-sian tails is greatly reduced for high-pT muons.

1. The pull is defined here as the difference between the reconstructed and generated parameter, normal-ised by the error on the reconstructed parameter.

Figure 5-7 Pulls in 1/pT for pT = 20 GeV muons,summed over all η: without pile-up (mean 0.008, r.m.s.1.10), with pile-up (mean 0.007, r.m.s 1.17) (iPa-tRec).

-4 -2 0 2 4

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20 GeV muon with pile-up20 GeV muon



5.1.2.2 Pions

There are much larger non-Gaussian tails in the case of pions because of hadronic interactions.To compare results with those shown in the b-tagging analysis (Section 6.7), the tail fractions inthe d0 distributions for pions have been studied after the application of the same cuts as used inthat work and Section 5.1.1.

The resulting tail fractions for d0 for pions of pT = 5 and pT = 20 GeV are shown in Figures 5-10and 5-11. These tail fractions are similar to those found for jets in the pattern recognition studiespresented in Section 5.2. This indicates that the source of the non-Gaussian tails is secondary in-teractions rather than pattern recognition errors.

Figure 5-8 Tail fractions for impact parameter as afunction of |η| for pT = 1 GeV muons.

Figure 5-9 Tail fractions for pT as a function of |η| forpT = 1 GeV muons.

Figure 5-10 Tail fractions for impact parameter as afunction of |η| for pT = 5 GeV pions.

Figure 5-11 Tail fractions for impact parameter as afunction of |η| for pT = 20 GeV pions.

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5.1.3 Fake rate

5.1.3.1 Definition of Fake Tracks

It is essential to consider some measure of the fake rate, since in the absence of any control, it ispossible to make the efficiency arbitrarily high. Fakes are notoriously difficult to define, and thiscan only be done meaningfully in the context of a particular physics analysis. Fake tracks inevi-tably are made up from bits of real tracks (usually pile-up tracks in the case of isolated tracksearches) and there is the possibility of a continuous range from perfectly reconstructed tracks,through tracks which are spoilt by varying amounts due to the presence of nearby tracks andnoise, to completely fake tracks which have hits from many different tracks with no single trackdominating.

For this work, fake tracks are defined as tracks where ≤ 50% of the precision hits come from onesingle KINE track alone. Cuts have been relaxed compared to section Section 5.1.1.1, otherwisethe fake rate is too small to study. The fake tracks which are considered should satisfy:

1. Number of precision hits ≥ 7, unless otherwise specified.

2. Number of pixel hits ≥ 2.

3. |d0| < 2.5 mm - this cut is implicit in iPatRec, and was made in xKalman to facilitatemeaningful comparison.

4. pT > 2 GeV.

While efficiency studies for isolated tracks have been performed for both zero and design lumi-nosity, studies of the fake rates are only useful in the presence of pile-up. Since only a modestnumber of pile-up events have been generated, to gather sufficient statistics for an analysis ofthe fake track rate, it is necessary to search over the complete acceptance of the tracker. The rateis normalised with respect a cone size of Δη = 0.2, Δφ = 0.2, which corresponds roughly to thearea associated with a cluster in the EM calorimeter by the Level-1 Trigger. For iPatRec, this isdone by dividing up each event with a large number of non-overlapping cones of the appropri-ate size. Allowance is made for the curvature of lower momentum tracks. For xKalman, patternrecognition is performed over the complete acceptance, and the observed rate is normalised by(2×2.5×2π)/(0.2×0.2).


Figures 5-12 and 5-13 show the fake rate for pT > 2 GeV, compared with the efficiencies for sin-gle pions (pT = 5 GeV) with pile-up - both distributions are shown as a function of the minimumnumber of precision hits on a track, starting at 6 hits for iPatRec and 4 for xKalman. For ≥ 7precision hits, the fake rates are O(10-3) and O(10-4) from iPatRec and xKalman, falling inboth cases to O(10-5) with requirement of ≥ 9 precision hits. These numbers can be comparedwith the rate of real tracks with pT > 2 GeV in the pile-up of 2 × 10-2.



Figure 5-14 shows the fake rate from xKalmanas a function of the fraction of TRT drift-timehits found on a track compared to the numberof straws crossed. If TRT hits are required fortracks from iPatRec, this corresponds ap-proximately to a requirement of ≥ 60% of TRThits in xKalman; in which case, for ≥ 6 preci-sion hits, both analyses see O(10-5) fakes.

With the default cuts for iPatRec or xKa-lman (see Section 2.5.2) or tighter cuts likethose in Section 5.1.1, the fake rate is too smallto begin to understand the nature of the faketracks. Therefore the cut on the number of pre-cision hits has been loosened. Figures 5-15and 5-16 show the fake rates as a function of|η|. The distributions have been plotted fornumbers of silicon precision hits ≥ 6 and ≥ 7.As this cut is raised and the fake rate is re-duced, it is not clear whether the shape of thedistributions will be the same. It is found thatmost of the fakes have only one or two hitscoming from any single track. xKalman sees more fakes at high |η| which is probably a reflec-tion of the high occupancy of the TRT straws in the long wheels.

Figures 5-17 and 5-18 show that the fake rates fall sharply when the pT threshold is increased.However, both algorithms have tails extending to higher momentum, although the tail fromiPatRec is much more significant. The fake tracks in the high-pT tail have been examined andare made from hits from several different tracks and do not correspond to genuine high-pTtracks.

Figure 5-12 Fake rates (open circles) and efficienciesfor pions with pT = 5 GeV (solid circles) as a functionof number of precision hits (6 to 15) (iPatRec).

Figure 5-13 Fake rates (open circles) and efficienciesfor pions with pT = 5 GeV (solid circles) as a functionof number of precision hits (4 to 15) (xKalman).

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5.1.4 Effect of Noise and Detector Inefficiency

Whilst all studies so far have been performed with values of detector efficiency and noise whichcorrespond to the current best understanding, it is inevitable that with irradiation, the perform-ance will degrade. Also, there will be failures of complete detector modules at some level. Previ-ous studies [5-1] showed that for noise occupancies above ~0.5% in the SCT, the rate of spoilttracks increases rapidly. In practice, the noise will be controlled by raising the thresholds, effec-tively reducing the hit efficiency. Some initial studies have indicated that even if the SCT detec-tor efficiency is degraded by as much as 20%, the change in the track finding efficiency forisolated tracks falls by only a few percent, while the fake rate is little changed. It would appearthat the tracker is robust against moderate changes in noise and detector efficiency, however

Figure 5-15 Fake rate as a function of |η| (iPatRec). Figure 5-16 Fake rate as a function of |η| (xKalman).

Figure 5-17 Fake rates as a function of the cut on pTabove 2 GeV (iPatRec).

Figure 5-18 Fake rates as a function of the cut on pTabove 1 GeV (xKalman).

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these studies need to be pursued for inefficiencies in all subdetectors and for more complicatedphysics processes, such as jets.

5.1.5 Comparison with Specifications

With respect to specification R1, it is clear that efficiencies well above 95% can be obtained forisolated muons, and do not appear to be affected significantly by pile-up. For isolated pionswith pT ≥ 5 GeV, the average efficiency is around or greater than 95% - but this is limited by ma-terial interactions, not by pattern recognition per se. It has been shown that the fake rate is read-ily reduced to O(10-2) of the rate of real tracks from pile-up, even with quite conservative cuts.

5.2 Tracks in Jets

While there are physics reasons for studying isolated tracks and they provide an indication ofthe detector performance, studies of the tracking within jets are much more challenging and canindicate limitations of the detector design. In this section, the reconstruction of withmH = 400 GeV is examined. The motivation for and physical characteristics of events like theseare discussed in Section 2.4.3. Such events are of interest since they mimic the backgrounds forb-tagging (see Section 6.7) and good pattern recognition is essential to avoid tails in the impactparameter distributions. This work builds on previous studies [5-2], where it was shown thatthe b-tagging at mH = 100 GeV was limited by physics and not the detector.

Since track reconstruction in high-pT jets is a challenging area for pattern recognition algo-rithms, a systematic comparison has been made between two of the three available algorithms,iPatRec and xKalman. This procedure has proven very useful in understanding the perform-ance of the present code and, more importantly, to reliably evaluate the detector performance it-self. For the first part of the work reported here, both algorithms have been used in a ‘cone’ ofΔR = 0.4 around each jet and the study has been limited to tracks with pT > 1 GeV.

5.2.1 Track Quality

The results of the b-tagging performance depend heavily on the track reconstruction efficiencyand on the quality of the reconstructed tracks which come out from the pattern recognition al-gorithm. For tracks in jets, this quality is evaluated based on the information from the pixel andSCT layers alone: each track crosses 3 pixel and 8 SCT layers (overlaps between adjacent mod-ules increase these numbers by about 10% - see Section 3.3). To illustrate the quality of the pat-tern recognition, three categories1 of precision layer hits associated to a reconstructed track aredefined:

• Unique Hit - hit which was produced uniquely by the one KINE track which producedthe majority of the precision hits associated to the reconstructed track.

• Spoilt Hit - hit which was produced by two or more KINE tracks, or by one KINE trackplus noise, or by pure noise.

1. The classifications are slightly weaker than the ideal, since it is technically difficult to identify the originof a hit when it arises from several sources.

H uu→



• Wrong Hit - hit which was produced by one and only one KINE track which was differentfrom the one which produced the majority of hits.

The default cuts used by both pattern recognition algorithms require ≥ 7 precision hits associat-ed to a track, at least one of which should come from the first two pixel detectors. In this section,results are presented after these default cuts, followed by results with some additional cuts,which were found to be necessary for the better b-tagging performance.

Figures 5-19 and 5-20 show the number of pixel hits associated to a track. Figure 5-19 shows thatan average of 3.22 pixel hits are associated to each track (includes overlaps, cf. Figure 3-31), outof which 3.1 are unique. The 3% of tracks (before quality cuts) with no unique hits in the pixelsarise from tracks produced in secondary interactions or from the decays of V0’s which start be-yond the pixel layers but have been associated with sufficient numbers of hits to be accepted bythe pattern recognition algorithm (see Section 2.5.2.1). (After the cuts described later, this 3% be-comes 0.8%.) Figure 5-20 shows that 3.6% of the tracks have at least one wrong hit associated tothem and 6.6% at least one spoilt hit, and of the wrong (spoilt) pixel hits, 83% (83%) are in theB-layer. In principle, it is possible to relate the number of spoilt hits to the number of mergedclusters shown in Figure 3-49. The fraction of tracks with spoilt hits should be roughly twice1

the sum of the fractions of merged hits on each pixel layer (correlations will reduce this).

Figures 5-21 and 5-22 show the number of SCT hits associated to a track. Figure 5-21 shows thatan average of 8.2 SCT hits are associated to each track (includes overlaps), out of which 7.9 areunique. Figure 5-22 shows that 1.9% of the tracks have at least one wrong hit associated to themand 17.2% at least one spoilt hit.

1. Usually each merged cluster corresponds to spoilt hits from two tracks.

Figure 5-19 Total number of pixel hits (solid line) andnumber of unique hits (dashed) associated to a recon-structed track (iPatRec).

Figure 5-20 Number of wrong (solid line) and spoiltpixel hits (dotted line) associated to a reconstructedtrack (iPatRec).

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Figure 5-23 shows the ratio of valid drift-timemeasurements in the TRT straws to the totalnumber of straw hits for each selected track.This ratio has an average value of 0.78 for thetracks in the u-jets (solid histogram) as com-pared to 0.91 for isolated tracks at low lumi-nosity (dashed histogram). These numbers canbe compared to the values shown inFigure 3-80 for the straw drift-time efficiencyversus luminosity: the average drift-time effi-ciency in the u-jets is close to that expectedfrom pile-up at the LHC design luminosity.Figure 5-23 also shows that a fraction of thetracks in u-jets are associated with very fewvalid drift-time measurements, correspond-ing to the densest part of the jet.

Figures 5-24 and 5-25 show the pulls of the pT and impact parameter distributions, respectively.Both exhibit Gaussian peaks with non-Gaussian tails caused by low quality tracks. In the case ofthe pull of 1/pT, the r.m.s is 50% greater than the Gaussian width.

In Table 5-2, the fraction of the tracks with pulls on 1/pT and impact parameter > 3 are given forvarious |η| bins, separately for primary and secondary tracks and for the two algorithms. Atrack which originates from the physics event is called a primary, while a track produced by de-tector interactions is called a secondary. The numbers of tracks in the tails clearly follow the

Figure 5-21 Total number of SCT hits (solid line) andnumber of unique hits (dashed) associated to a recon-structed track (iPatRec).

Figure 5-22 Number of wrong (solid line) and spoiltSCT hits (dotted line) associated to a reconstructedtrack (iPatRec).

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material profile of the Inner Detector. The non-Gaussian multiple (Coulomb) scattering contri-bution is proportional to the logarithm of the material thickness traversed. The impactparameter is sensitive to the material of the innermost layers; whereas the momentum is sensi-tive to the total amount of material traversed by the track. This explains the bigger momentumtails compared to the impact parameter ones. The significantly bigger tails for the secondariesare mostly due to confusion in the B-layer itself, as discussed later.

Figures 5-26 and 5-27 show the fit χ2 probability for tracks in jets from iPatRec and xKalmanrespectively (the histograms are normalised to one). The χ2 contains contributions from the de-tector resolution and material. In the reconstruction, the material has been approximated as aseries of layers with the appropriate thickness uniformly distributed in φ. This will underesti-mate the local concentrations of material in the simulation,1 causing the nominal track errors tounderestimate the actual spread in the reconstructed parameters, and hence giving rise to trackswith low probability. An additional approximation is the representation of multiple scattering

1. Also, the simulation will tend to underestimate the ‘lumpiness’ which is present in the real detector.

Figure 5-24 Pull of 1/pT for tracks in jets (iPatRec).R.m.s. is 1.49, Gaussian width is 1.03.

Figure 5-25 Pull of d0 for tracks in jets (iPatRec).R.m.s. is 1.30, Gaussian width is 1.00.

Table 5-2 Fraction of tracks with pulls on 1/pT and impact parameter > 3.

|η| Tails in 1/pT (%) Tails in d0 (%)


Primaries Secon. Primaries Secon. Primaries Secon. Primaries Secon.

0.0-0.5 3.3±0.1 37.3±1.1 3.0±0.1 45±2 2.6±0.1 50.3±1.3 3.1±0.1 55±2

0.5-1.0 3.6±0.1 36.1±1.1 3.4±0.1 42±2 2.6±0.1 45.8±1.2 3.2±0.1 47±2

1.0-1.5 4.2±0.1 45.6±1.1 3.7±0.2 51±2 3.0±0.1 53.9±1.1 4.1±0.2 60±2

1.5-2.0 5.0±0.1 51.2±1.1 3.4±0.2 53±1 3.9±0.1 61.7±1.1 4.7±0.2 60±2

2.0-2.5 4.1±0.1 33.7±1.2 3.1±0.2 42±2 3.5±0.1 36.9±1.2 3.7±0.2 37±2

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by a Gaussian distribution. The net effect is to modify the fit χ2 probability from a flat distribu-tion to one with a small slope towards higher probabilities, compensated by a spike at low prob-abilities. There is a significant additional contribution to the low probability spike from trackswith spoilt and wrongly associated hits. The shaded areas in the figures show the fit χ2 proba-bility for the primary tracks whose hits were all categorised as unique. The figures show that thelow probability spike is significantly smaller for this class of tracks.

Very important aspects of the pattern recognition performance are the track reconstruction effi-ciency and the fraction of fake tracks. Figures 5-28 and 5-29 show the primary track reconstruc-tion efficiency as a function of |η| from iPatRec and xKalman respectively. Thesuperimposed line represents one minus the material distribution (absorption length) up to thesecond SCT layer, as a function of |η|. From the same figures, the average track reconstructionefficiency is calculated to be 93% for iPatRec and 89% for xKalman. Figures 5-30 and 5-31show the fraction of fakes. Here a fake track is defined either as corresponding to the sameKINE track as another reconstructed track, or as having < 50% unique hits. The effect of the ma-terial distribution in the detector is again clear in this distribution. The average fraction of fakesover all |η| was calculated to be 0.5% for iPatRec and 0.7% for xKalman.

The effect of the material can be seen also in Figures 5-32 and 5-33, where the fractions of tracksproduced by detector interactions (secondaries) is plotted. The fraction of secondaries, aver-aged over all |η|, was calculated to be 4.1% for iPatRec and 6.4% for xKalman. xKalman re-constructs ~50% more secondaries than iPatRec, because it is more sensitive to secondaryinteractions produced at the outer radii of the precision tracker and in the TRT. As it will beshown later (and can be seen from the tails in Table 5-2), the presence of the low quality tracksand of the secondaries degrades the b-tagging performance. Therefore, selection cuts have to beimposed to reduce these tracks without significantly deteriorating the efficiency of the primaryevent tracks.

Figure 5-26 Fit χ2 probability for tracks in jets (iPa-tRec).

Figure 5-27 Fit χ2 probability for tracks in jets (xKa-lman).

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5.2.2 Selection Cuts for b-Tagging

The studies reported in this section, Section 5.2, are motivated by the wish to understand as ac-curately as possible the Inner Detector performance in terms of b-tagging, as discussed inSection 6.7. For this reason a more systematic study of the track reconstruction performance inhigh-pT jets has been performed with cuts chosen for optimal b-tagging performance. Theserely in particular on the B-layer itself to obtain the best possible impact parameter resolutionand reject tracks with impact parameters which are too large.

Figure 5-28 Reconstruction efficiency of the primarytracks as a function of |η|. The superimposed line rep-resents the material up to the second SCT layer (seetext) (iPatRec).

Figure 5-29 Reconstruction efficiency of the primarytracks as a function of |η| (xKalman).

Figure 5-30 Fraction of fakes as a function of |η|(iPatRec).

Figure 5-31 Fraction of fakes as a function of |η|(xKalman).

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To understand and hence improve the quality of the reconstruction, the reconstructed track pa-rameters have been compared with those from the original Monte Carlo tracks. The matching χ2

probability is shown in Figures 5-34 and 5-35 for iPatRec and xKalman respectively. Thepoorly reconstructed tracks are clearly visible with a probability close to 0. Tracks whose proba-bility is < 0.04 are classified as spoilt tracks. These spoilt tracks represent 10% of the totalnumber of reconstructed tracks. It was found that ~30% of them were secondaries; ~30% wereprimary tracks with at least one spoilt or wrong hit associated to them and the rest (~40%) werebadly reconstructed primary tracks with all their hits unique.

Figure 5-32 Fraction of secondaries as a functionof |η| (iPatRec).

Figure 5-33 Fraction of secondaries as a functionof |η| (xKalman).

Figure 5-34 Matching χ2 probability for tracks in jets(iPatRec).

Figure 5-35 Matching χ2 probability for tracks in jets(xKalman).

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Figures 5-36 and 5-37 show the ratios of the number of precision layer hits and number of pixelhits for spoilt tracks compared with all tracks. Figure 5-38 shows that only 1% of the primarytracks (solid line) do not have an associated B-layer hit, in comparison to 27% of the secondarytracks (dotted line). Figure 5-39 shows that only 0.7% of the primary tracks (solid line) have|d0| ≥ 1 mm, in comparison to 30% of the secondary tracks (dashed line) and to 5% of thetracks produced in a B-vertex (dotted line).

Figure 5-36 Ratio of number of precision hits forspoilt tracks compared with all tracks (iPatRec).

Figure 5-37 Ratio of number of pixel hits for spoilttracks compared with all tracks (iPatRec).

Figure 5-38 Presence of hits on the B-layer for theprimary (solid line) and secondary (dotted line) tracks(iPatRec).

Figure 5-39 Impact parameter distribution of the pri-mary (solid line), B-tracks (dotted line) and secondar-ies (dashed line) (iPatRec).

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From these distributions, the following selection cuts have been derived:

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3. At least one associated hit in the B-layer.

4. |d0| ≤ 1 mm.

The fractions of tracks with at least one wrong or spoilt hit after the track quality cuts are shownin Table 5-3, and compared with the numbers from before the cuts. The cuts help remove trackswith wrong hits, but retain tracks with spoilt hits, since these hits are largely correct.

By design, the cuts improve the matching χ2 distribution - 60% of those tracks removed arespoilt tracks. Because they are related to the matching χ2, the tails of the pulls of the pT and im-pact parameter distributions are improved, as seen in Table 5-4.

In Table 5-4, it can be seen that the secondary tracks1 still exhibit very long tails, while those ofthe primary tracks are significantly reduced. This effect is due to secondary tracks which wereproduced after the B-layer but had a B-layer hit incorrectly associated to them. Indeed, > 90% ofthe secondaries produced after the B-layer2 have impact parameter pulls > 3, in comparisonwith 21% of the secondaries produced on and before the B-layer. Figures 5-40 and 5-41 show the|η| distribution of the fraction of secondaries which passed the selection cuts and were pro-duced on and before the B-layer, for iPatRec and xKalman respectively. The superimposedline demonstrates the fact that the |η| distribution of this kind of secondary is a result of the1/sinθ distribution of the material in the beam pipe and the B-layer.

1. Before the cuts, secondaries account for 46% of the tails, and 31% after the cuts.2. This category of secondaries represents 33% of the total number of secondaries passing the selection

cuts.

Table 5-3 Fraction of tracks with wrong and spoilt hits in jets.

Before quality cuts After quality cuts

Wrong (%) Spoilt (%) Wrong (%) Spoilt (%)

Pixels 3.6 6.6 1.4 6.0

SCT 1.9 17.2 1.2 16.9

Table 5-4 Fraction of tracks with pulls on 1/pT and impact parameter > 3 after the cuts.



Primaries Secon. Primaries Secon. Primaries Secon. Primaries Secon.

0.0 to 0.5 2.7±0.1 28.5±1.6 2.5±0.1 42±4 1.8±0.1 42.5±1.9 2.2±0.1 44±4

0.5 to 1. 2.9±0.1 27.8±1.5 2.8±0.1 44±4 1.8±0.1 38.7±1.8 2.1±0.1 32±4

1.0 to 1.5 3.4±0.1 35.1±1.5 2.8±0.2 44±4 1.9±0.1 43.7±1.7 2.5±0.1 39±3

1.5 to 2.0 3.9±0.1 44.0±1.6 2.8±0.2 52±3 2.3±0.1 54.7±1.8 2.3±0.2 41±3

2.0 to 2.5 3.2±0.1 30.2±1.6 2.3±0.2 40±3 2.2±0.1 32.4±1.7 2.2±0.2 27±3



Figures 5-42 and 5-43 show the |η| distribution of the fraction of secondaries which passed theselection cuts and were produced after the B-layer, for iPatRec and xKalman respectively. Inthese plots, the |η| distributions of the secondaries clearly follow the material of the Inner De-tector after the B-layer.

Figure 5-40 Fraction of secondaries surviving thecuts and produced on and before the B-layer as afunction of |η|. The superimposed line represents the1/sinθ distribution of the material (iPatRec).

Figure 5-41 Fraction of secondaries surviving thecuts and produced on and before the B-layer as afunction of |η| (xKalman).

Figure 5-42 Fraction of secondaries surviving thecuts and produced after the B-layer as a function of |η|(iPatRec).

Figure 5-43 Fraction of secondaries surviving thecuts and produced after the B-layer as a function of |η|(xKalman).

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Figures 5-44 to 5-49 show, after imposing the selection cuts on the tracks, a) the primary trackreconstruction efficiency, b) the fraction of fakes and c) the fraction of secondaries as a functionof |η|. After imposing the selection cuts for iPatRec, the average efficiency for the primarytracks drops from 93% to 88%, while the fraction of secondaries is reduced to the level of 1.8%and fakes are almost eliminated (0.1%). For xKalman, the same cuts reduce the average efficien-cy for the primary tracks from 88.8% to 86.3%, with 1.7% of secondaries and 0.2% of fakes.

Figure 5-44 Reconstruction efficiency of the primarytracks as a function of |η| after imposing the selectioncuts (iPatRec).

Figure 5-45 Reconstruction efficiency of the primarytracks as a function of |η| after imposing the selectioncuts (xKalman).

Figure 5-46 Fraction of fakes as a function of |η| afterimposing the selection cuts (iPatRec).

Figure 5-47 Fraction of fakes as a function of |η| afterimposing the selection cuts (xKalman).

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Figures 5-50 and 5-51 show the reconstruction efficiency for tracks in a jet as a function of dis-tance to the closest KINE track in η−φ for iPatRec and xKalman respectively. Some loss of re-construction efficiency for nearby tracks is to be expected from the detector properties, but thereis also a significant contribution from the pattern recognition algorithms.

Figures 5-52 and 5-53 show the reconstruction efficiency for tracks in a jet as a function of thetrack pT for iPatRec and xKalman respectively. Some loss of efficiency on low-pT tracks is dueto threshold effects, when looking for tracks above pT = 1 GeV.

Figures 5-54 and 5-55 show the reconstruction efficiency as a function of the jet track multiplici-ty for iPatRec and xKalman respectively. The small loss of efficiency for low multiplicity jetsfor iPatRec is due to edge effects for tracks produced near the road boundaries.

Figure 5-48 Fraction of secondaries as a function of|η| after imposing the selection cuts (iPatRec).

Figure 5-49 Fraction of secondaries as a function of|η| after imposing the selection cuts (xKalman).

Figure 5-50 Reconstruction efficiency for tracks in ajet as a function of distance to the closest KINE track(iPatRec).

Figure 5-51 Reconstruction efficiency for tracks in ajet as a function of distance to the closest KINE track(xKalman).

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Figure 5-52 Reconstruction efficiency for tracks in ajet as a function of track pT (iPatRec).

Figure 5-53 Reconstruction efficiency for tracks in ajet as a function of track pT (xKalman).

Figure 5-54 Reconstruction efficiency as a function ofthe jet track multiplicity (iPatRec).

Figure 5-55 Reconstruction efficiency as a function ofthe jet track multiplicity (xKalman).

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The effect of a quality cut on the fit χ2 proba-bility has also been studied. Excluding trackswith fit χ2 probability smaller than 1%, the av-erage track reconstruction efficiency was cal-culated to be 86% and the fraction ofsecondaries 1.4%. The fraction of secondariesas a function of |η| is shown in Figure 5-56.Such a cut also will reduce the tails on the pulldistributions, as it is shown in Table 5-5.

Table 5-5 Fraction of tracks with pulls on 1/pT and impact parameter > 3 after imposing the fit χ2 probability cut(iPatRec).


Primaries Secondaries Primaries Secondaries

0.0 to 0.5 1.9±0.1 19.6±1.5 1.5±0.1 30.1±1.8

0.5 to 1. 2.0±0.1 21.7±1.5 1.5±0.1 29.2±1.7

1.0 to 1.5 2.3±0.1 28.6±1.5 1.5±0.1 34.2±1.7

1.5 to 2.0 2.7±0.1 38.5±1.8 1.8±0.1 42.1±1.8

2.0 to 2.5 2.3±0.1 26.4±1.7 1.9±0.1 24.1±1.6

Figure 5-56 Fraction of secondaries as a function of|η| after cutting on the fit χ2 probability (iPatRec).

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5.2.3 Conclusions on Pattern Recognition in Jets

Despite the different approaches to pattern recognition taken by the algorithms compared here,iPatRec and xKalman, the results are in a good agreement, indicating that they reflect directlythe underlying physics and the performance of the detector itself. In particular, the reconstruc-tion efficiencies for primary tracks is found to be about 88% averaged over all η, with most ofthe losses being due to the material in the detector. The fake track rates are well below 1% andthe badly reconstructed tracks amount to a few per cent of the total number of reconstructedtracks, as estimated from the non-Gaussian tails in the impact parameter distribution.

A particular source of concern is the impact of reconstructed tracks from secondary interactionsin the first layers of the precision tracker system. Most of the tracks have a large impact param-eter and therefore increase the probability of tagging any jet as a b-jet. About 30% of these tracksoriginate from a point beyond the B-layer, which indicates that for 0.6% of the reconstructedtracks, confusion in the B-layer itself is the cause for fake b-jet tags.

5.3 References

5-1 SCT Backup Document, ATLAS Internal Note, INDET-NO-085.



6 Physics Studies 145

6 Physics Studies

6.1 High-pT Electrons and QCD-Jet Rejection

The understanding of isolated high-pT electrons will be essential for physics at the LHC, in par-ticular the searches for leptonic decays of the Higgs boson and new vector bosons (W′ and Z′),and also the extraction of clean samples of tt events for the measurement of mtop. In the ATLASLetter of Intent [6-1], it was pointed out that at the LHC, the isolated electron-to-jet ratio is ex-pected to be O(10-5) at pT ~20-40 GeV. Thus, in addition to the nominal jet rejection factor of102−103 coming from the EM calorimeter [6-2], a further significant reduction must be providedby the Inner Detector [6-3][6-4]. This section describes a study of inclusive electron reconstruc-tion efficiency and rejection capability against QCD-jets, using the combined information fromthe ATLAS calorimeter and Inner Detector. The work described here builds on a previous studyperformed on an old layout [6-5] and is aimed at low luminosity physics.

6.1.1 Datasets

The PYTHIA event generator has been used to generate a large sample of events containinghard-scattering (high-pT) processes with pT > 17 GeV and |η| < 2.7. This sample consistsmainly of di-jet events (referred to as QCD-jets), including initial and final state radiation proc-esses. In addition, other physics processes such as prompt photon, heavy quark and intermedi-ate vector boson production were also included, according to their cross-sections. More detailscan be found in [6-5][6-6]. The total summed cross-section from the various sub-processes is~0.5 mb. Throughout this section, the above mentioned processes are referred to collectively asthe jet sample. A total of 5 × 105 generated events, corresponding to approximately 3 × 105 jetswith pT > 17 GeV, within |η| < 2.7, have been analysed.

Electron datasets consisting of single electrons have been generated for pT = 20 and 40 GeV. Theeffect of pile-up on single electrons is to reduce their isolation, and hence the efficiency withwhich they can be identified. In order to study the consequences of going from low to design lu-minosity, electron datasets for pT = 20 and 40 GeV with pile-up corresponding to 1034 cm-2s-1

have been generated also.

6.1.2 Event Selection and Analysis

6.1.2.1 Calorimeter Selection

For the jet sample, a simple particle-level filter was applied to reduce the amount of CPU-inten-sive GEANT simulation. This filter does not bias in any way the results of the analysis presentedhere. After the GEANT simulation, the events were processed through additional filter cuts rep-resentative of the Level-1 trigger. After these cuts, the remaining events were mainly QCD-jetswith a large fraction of their energy carried by electromagnetically-showering particles, domi-nantly π0 and η mesons. These were reduced further by the following sequential cuts represent-ative of the Level-2 calorimeter trigger:


146 6 Physics Studies

1. ET > 17 GeV, where ET applies to all electromagnetic (EM) clusters in the event.

2. ET(Hcal) < 0.7 GeV, which measures the leakage into the hadronic calorimeter directly be-hind the EM cluster.

3. E3×7/E7×7 > 0.85, where E3×7 (E7×7) is the energy deposited in the second sampling in acluster of 3×7 (7×7) cells in η×φ in the EM calorimeter. The isolation in the EM calorimeteris defined as 1−E3×7/E7×7.

4. Cluster profile in the EM calorimeter. The cluster width in |η| is calculated (in the sec-ond sampling) with an energy weighted sum over all the cells contained in a 3×5 (η×φ)cluster in the EM calorimeter. This width depends on the position of the cluster in the cell,and a cut is placed requiring the cluster width to lie within an allowed band.

The distributions of these quantities are shown in Figures 6-1 to 6-4 for i) single electrons withpT = 20 GeV, ii) electrons with pile-up added, and iii) the jet sample events. For the electronsand electrons with pile-up, the distributions are shown sequentially after each cut. However, forthe jet sample, all the calorimeter trigger cuts have already been applied (for technical reasons).

Figure 6-1 shows the ET distributions (as measured by the nominal 3×7 cluster of EM calorime-ter cells), for all ‘seed’ clusters1 with ET > 5 GeV. Additional low-ET clusters from pile-up parti-cles which satisfy this cut can be seen in the second plot. In the jet sample (third plot), theLevel-2 trigger cut at 17 GeV, is prominent, and again low-ET clusters in the events passing this

1. These clusters measure the energy in a 5×5 cluster, hence the energy is not identical to that measured ina 3×7 cluster.

Figure 6-1 ET of EM clusters in event. Figure 6-2 ET in hadron calorimeter cells behind theEM cluster. Electrons are shown after theET > 17 GeV cut, and the jets after all cuts.

0

2000

0 10 20 30 40 50

ET (GeV)

Electrons

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10 4

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Electrons+pile-up

1

10 210 3

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Jets



cut can be seen. Figure 6-2 shows the distribution of ET in the hadronic calorimeter directly be-hind the EM cluster. The jet sample shows a broad distribution, arising from the energy deposit-ed by the high-pT hadrons, which is truncated by the trigger cut at 0.7 GeV. For the electronswith pile-up, a significant high energy tail remains, with ~7% of the events beyond the cut.Figure 6-3 shows the EM isolation. Again, the jet spectrum is seen to be truncated by the isola-tion cut at 0.15, which is very efficient for electrons with and without pile-up. Figure 6-4 showsthe cluster widths.

Table 6-1 gives a summary of the efficiencies after the calorimeter cuts for electrons of pT = 20and 40 GeV, before and after pile-up is added, and of the rejection factors for jets. The results areshown for four intervals of |η|, which are intended to characterise the different amounts of ma-terial in the Inner Detector and the cracks in the EM calorimeter [6-2]. The small |η| intervalbetween 1.37 and 1.52, corresponding to the EM calorimeter transition region between the bar-rel and the end-cap, has been excluded from this analysis since it contains too much passive ma-terial (cryostat, flanges) for precision EM calorimeter measurements. Whereas the jet rejectionfactors include the effects of the filter cuts, the electron efficiencies do not. However, it has beenverified that the filter cuts are ~99% efficient for electrons of 20 and 40 GeV. The electron effi-ciency is on average ~5% better for pT = 40 GeV than for pT = 20 GeV at high luminosity. Afterall calorimeter cuts, the rejection factor against events from the jet sample (within the detectoracceptance) is ~150. Note that the higher rejection factor reported in [6-2][6-5] resulted from nor-malising to the total number of jets generated. Although the partons were generated withpT ≥ 17 GeV, after final state radiation and hadronisation the jet energy may be reduced. There-fore for this study, the rejection has been normalised to the total number of jets withET > 17 GeV reconstructed at particle-level using the fast simulation package ATLFAST [6-7].This is believed to give a better reflection of the rejection achieved by ATLAS. Also, the calorim-

Figure 6-3 Isolation of EM clusters. Electrons areshown after the ET > 17 GeV and ET(had) < 0.7 GeVcuts, and the jets after all cuts.

Figure 6-4 Shower width in η as a function of the rel-ative position in η in the cell.

0

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Electrons

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th Electrons

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Wid

th Jets



eter cuts have not been fully optimised, and there is some hope for improvement, especiallyfrom the use of the η-strips.

6.1.2.2 Track Reconstruction and Selection

At this stage of the analysis, the jets consist mainly of high-pT π0 and η mesons and the expectedcharged track multiplicity is low. Further reduction of the jet backgrounds can therefore beachieved by requiring the presence of a charged track pointing to the EM cluster, with a recon-structed track momentum consistent with the measured cluster energy.

For this study, two track reconstruction packages, xKalman and iPatRec, have been used (seeSection 2.5.2). Owing to differences between the two algorithms, the Δη×Δφ ‘cones’ used for thetrack search around the EM cluster centroid are 0.3×0.2 for xKalman, and 0.1×0.1 for iPatRec.Only tracks with pT > 1 GeV have been kept. A bremsstrahlung recovery procedure is used inboth packages. In xKalman, this is done by combining in 3-D the standard track parameters(obtained from a fit which allows for multiple scattering and dE/dx - see Section 2.5.2.3), withthe position of the calorimeter cluster centroid. In iPatRec, an alternative track fit is madewhich includes the calorimeter centroid as an additional measurement [6-3]. This fit allows for asingle discrete increase in curvature corresponding to a possible hard bremsstrahlung, with themomenta of the track segments being measured before and after the break-point. For both pro-grams, these fits are referred to as the brem-fits1.

Results for electron efficiencies before and after the addition of pile-up, and for jet rejection, arepresented for both reconstruction algorithms. The convention used to present the results is:xKalman value (iPatRec value). In order to permit a realistic comparison of the results, thefollowing selection cuts have been used in both programs:

1. Number of precision hits ≥ 9.


3. pT > 5 GeV, evaluated for the complete track or on the first segment in the case of abremsstrahlung hypothesis. This emulates the Level-2 track trigger requirement.

4. 0.7 < E/p < 1.4, where E is measured in the EM calorimeter and p in the Inner Detector.

1. For xKalman, this is a little confusing since the fit which allows for changes of track curvature (seeSection 2.5.2.3) is also referred to as the ‘brem-fit’.

Table 6-1 Electron efficiencies and jet rejection factors after application of the calorimeter selection criteria.

|η|

Efficiencies (%) Rejection

Electrons pT = 20 GeV Electrons pT = 40 GeV Jets

No pile-up With pile-up No pile-up With pile-up

0.00 - 0.70 98.7 ± 0.2 86.6 ± 1.5 98.8 ± 0.2 91.9 ± 1.2 165 ± 6

0.70 - 1.37 98.8 ± 0.2 92.1 ± 1.2 99.9 ± 0.1 95.6 ± 0.9 132 ± 5

1.52 - 2.00 97.4 ± 0.4 83.1 ± 2.0 99.2 ± 0.2 94.4 ± 1.1 137 ± 7

2.00 - 2.50 98.3 ± 0.3 91.2 ± 1.4 98.4 ± 0.3 94.4 ± 1.2 168 ± 9

All 98.4 ± 0.1 88.5 ± 0.8 99.1 ± 0.1 94.0 ± 0.6 148 ± 3



The reconstructed pT distributions for the pT = 20 GeV electrons, after track quality cuts (thefirst two cuts) but before a pT cut, are shown in Figures 6-5 and 6-6, for xKalman and iPatRecrespectively. The distributions are shown for the |η| intervals with the least and the most mate-rial, before and after the bremsstrahlung fits. For the lower |η| interval, corresponding to thebarrel region, both programs are able to make a successful correction for the bremsstrahlungtail. However, at the higher values of |η|, in the presence of more material, although both pro-grams are seen to make a substantial improvement to the bremsstrahlung tail, there remainmany events with significantly wrong momenta. The distributions of pT before the brem-fitfrom xKalman are a little bit more symmetric than those of iPatRec, because xKalman al-ready has some correction for bremsstrahlung in the track fitting as part of the Kalman fil-ter-smoother procedure, as was described in Section 2.5.2.3.

The pT distributions for the electrons with pile-up and for the jets are shown in Figures 6-7and 6-8. Again, the distributions are shown after track quality cuts, but before a pT cut, andshow the momenta of all tracks in the cones with pT > 1 GeV. Even in the presence of pile-up,the electron efficiency can be seen to remain very high for pT > 5 GeV. For the jets, the largernumber of low-pT tracks found by xKalman compared with iPatRec, is due to the largersearch cone. The majority of these tracks are removed by the pT cut.

Figure 6-5 Reconstructed pT of electron (generated pT = 20 GeV) (xKalman).

0

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0 25 50

xKalmanwithout brem fit0.0≤|η|≤0.7

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pT (GeV)

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pT (GeV)



Figure 6-6 Reconstructed pT of electron (generated pT = 20 GeV) (iPatRec).

Figure 6-7 Reconstructed pT after track quality cuts,of electrons with pile-up (open) and jets (shaded)(xKalman).

Figure 6-8 Reconstructed pT after track quality cuts,of electrons with pile-up (open) and jets (shaded)(iPatRec).

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After the quality cuts placed on the reconstructed tracks, the final selection required that the re-constructed track pT matched the EM calorimeter cluster ET. The xKalman and iPatRec distri-butions of E/p for both electrons and jet events, after the bremsstrahlung fits, are shown for tworegions of |η| in Figures 6-9 and 6-10. The pT resolution of the Inner Detector, which alreadydominates the width of the E/p distribution in the barrel region, further degrades as the materi-al thickness traversed increases. As a result, the 0.7 < E/p < 1.4 selection also suffers degrada-tion of efficiency with the increase of material, even though the bremsstrahlung fit corrects themomenta of many of the events in the tails of this distribution.

Summaries of the efficiencies obtained for electrons before and after bremsstrahlung correction,using xKalman and iPatRec, are presented in Tables 6-2 and 6-3 respectively. The values forthe electron efficiencies as a function of |η|, for the two programs, are seen to be compatible,both before and after the addition of the pile-up.

Figure 6-9 E/p after track cuts and brem fit for elec-trons (open) and jets (shaded) (xKalman).

Figure 6-10 E/p after track cuts and brem fit for elec-trons (open) and jets (shaded) (iPatRec).

0

20

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xKalman

0.0≤|η|≤0.7

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0.0≤|η|≤0.7

E/p

0

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20

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iPatRec

1.52≤|η|≤2.0

E/p



Table 6-2 Electron reconstruction efficiencies from xKalman. The track cuts correspond to the first three cutslisted in Section 6.1.2.2. The E/p efficiencies are evaluated relative to the track cuts; ‘All cuts’ include both calo-rimeter and tracking cuts.

|η|

Electron efficiency (%)

Track cuts E/p match E/p + brem fit All cuts

No pile-up No pile-up With pile-up

pT = 20 GeV

0.00 - 0.70 96.6 ± 0.3 96.0 ± 0.4 97.6 ± 0.3 93.1 ± 0.5 76.7 ± 1.8

0.70 - 1.37 94.5 ± 0.5 92.9 ± 0.5 94.2 ± 0.5 87.9 ± 0.7 82.0 ± 1.7

1.52 - 2.00 94.7 ± 0.5 87.2 ± 0.8 91.2 ± 0.7 84.2 ± 0.8 68.8 ± 2.5

2.00 - 2.50 81.6 ± 0.9 89.3 ± 0.8 97.8 ± 0.4 78.5 ± 0.9 67.0 ± 2.4

All 92.4 ± 0.3 92.0 ± 0.3 95.4 ± 0.2 86.6 ± 0.4 74.6 ± 1.0

pT = 40 GeV

0.00 - 0.70 97.5 ± 0.3 93.9 ± 0.4 98.2 ± 0.2 94.6 ± 0.4 83.1 ± 1.6

0.70 - 1.37 96.0 ± 0.3 91.1 ± 0.5 95.1 ± 0.4 91.2 ± 0.5 83.7 ± 1.6

1.52 - 2.00 97.0 ± 0.4 82.2 ± 0.8 91.3 ± 0.6 87.8 ± 0.7 79.9 ± 2.0

2.00 - 2.50 84.5 ± 0.8 86.4 ± 0.8 97.2 ± 0.4 80.9 ± 0.8 71.7 ± 2.4

All 94.3 ± 0.2 89.1 ± 0.3 95.6 ± 0.2 89.3 ± 0.3 80.3 ± 0.9



6.1.3 Jet Rejection Rates

In Section 6.1.2, the focus was on developing selection cuts to reduce the rate from the QCD-jetbackground, while retaining a good efficiency for identifying high-pT electrons. This sectioncontains a study of the nature of the events in the jet sample which survive the selection proce-dure. This leads to an evaluation of the background to the inclusive electron sample.

The jet sample events described in Section 6.1.1 were processed with xKalman and iPatRec inan identical way to the electron candidates. The overall rejection factors after each of the succes-sive selection criteria of calorimeter cuts, high-pT track requirements and E/p match includingbremsstrahlung recovery, are shown as a function of |η|, in Table 6-4, for both xKalman andiPatRec. It can be seen that a total reduction factor of ~17 (~13) is achieved by the track selec-tion.

In order to study the jet sample rejection in more detail, the events were classified into threeclasses based on generation level information (GENZ)1 for the calorimeter selection, and thenkinematic and particle information (KINE)2 once the highest pT track associated to the clusterhad been found. This classification provides the explanation of the calorimetric energy and theidentification of the associated charged particle, respectively.

1. Before the decay of long lived particles and the simulation of interactions in the material of the detector.2. Including decays and interactions.

Table 6-3 Electron reconstruction efficiencies from iPatRec. The track cuts correspond to the first three cutslisted in Section 6.1.2.2. The E/p efficiencies are evaluated relative to the track cuts; ‘All cuts’ include both calo-rimeter and tracking cuts.

|η|

Electron efficiency (%)

Track cuts E/p match E/p + brem fit All cuts

No pile-up No pile-up With pile-up

pT = 20 GeV

0.00 - 0.70 95.0 ± 0.4 95.5 ± 0.4 97.9 ± 0.3 91.8 ± 0.5 80.3 ± 1.7

0.70 - 1.37 92.1 ± 0.5 92.7 ± 0.5 96.5 ± 0.4 87.8 ± 0.7 82.8 ± 1.7

1.52 - 2.00 89.2 ± 0.7 77.0 ± 1.0 91.3 ± 0.7 79.3 ± 0.9 68.0 ± 2.5

2.00 - 2.50 78.3 ± 0.9 87.3 ± 0.9 91.5 ± 0.7 70.5 ± 1.0 61.7 ± 2.4

All 89.4 ± 0.3 89.4 ± 0.3 94.9 ± 0.2 83.5 ± 0.4 74.6 ± 1.0

pT = 40 GeV

0.00 - 0.70 94.8 ± 0.4 93.0 ± 0.5 97.8 ± 0.3 91.6 ± 0.5 85.4 ± 1.5

0.70 - 1.37 90.6 ± 0.5 90.6 ± 0.5 96.6 ± 0.3 87.4 ± 0.6 81.5 ± 1.7

1.52 - 2.00 91.4 ± 0.6 73.5 ± 0.9 88.9 ± 0.7 80.6 ± 0.8 73.8 ± 2.2

2.00 - 2.50 80.1 ± 0.8 83.1 ± 0.9 88.8 ± 0.7 70.0 ± 1.0 64.2 ± 2.5

All 89.8 ± 0.3 86.2 ± 0.3 93.9 ± 0.2 83.5 ± 0.4 77.4 ± 1.0



After Calorimeter SelectionThe cluster was associated to the highest pT GENZ particle pointing to the cluster. The threeclasses are:

• e corresponding to an electron, including signal processes from heavy quark decays andW/Z production,

• ‘γ ‘ corresponding to a photon, predominantly those from π0’s and including those whichsubsequently convert,

• ‘h’ corresponding to a hadron.

After Track Selection and E/p MatchingThe associated charged track was associated by its precision tracker hits to a KINE particle. Thethree classes are:

• e as above,

• γ(e+e-) corresponding to a conversion electron or Dalitz decay,

• h± corresponding to a charged hadron1.

The observed rates for these processes, normalised as described earlier, are presented inTables 6-5 and 6-6, for xKalman and iPatRec respectively. These results indicate that a largefraction of the calorimeter clusters labelled as ‘γ ’, have an associated high-pT charged hadronwhich is reconstructed by xKalman/iPatRec, and thereby labelled h± after the track selection.Only a small fraction of these clusters are found with a reconstructed track from an electroncoming from a photon conversion. The electrons are an irreducible background to high-pT elec-trons from new physics, but in the remainder of this section, will be considered to be the signalfor inclusive electron studies.

As discussed above, after the calorimeter selection, the dominant background consists of pho-tons from π0 and η decays. Τhis is significantly reduced by requiring the presence of a high-pTtrack. After the E/p match, charged hadrons remain as the main background. The final sig-nal-to-background ratio is ~1:3 (~1:4), for a QCD-jet rejection rate of ~2.5 × 103 (~2.0 × 103). The

1. These can give electron signatures when a π± overlaps with a γ or when a π± undergoes a charge ex-change process in the material in the vicinity of the EM calorimeter: π+n→π0p or π−p→π0n.

Table 6-4 Overall jet sample rejection factors for xKalman and iPatRec. Rejections include effects of previouscuts.

|η|

Jet rejection factors (102)

xKalman iPatRec

After caloselection

After trackselection

After E/p match After trackselection

After E/p match

0.00 - 0.70 1.65 ± 0.06 5.45 ± 0.39 28.3 ± 4.6 8.20 ± 0.72 22.4 ± 3.2

0.70 - 1.37 1.32 ± 0.05 4.06 ± 0.26 19.1 ± 2.6 4.78 ± 0.33 13.2 ± 1.5

1.52. - 2.00 1.37 ± 0.07 3.95 ± 0.32 26.7 ± 5.6 5.89 ± 0.58 22.7 ± 4.4

2.00 - 2.50 1.68 ± 0.09 6.22 ± 0.65 33.3 ± 8.1 6.66 ± 0.72 40.5 ± 10.8

All 1.48 ± 0.03 4.72 ± 0.18 25.0 ± 2.2 6.16 ± 0.27 19.8 ± 1.6



signal is predominantly from semi-leptonic decays of heavy quarks, and hence for isolated elec-trons from W and Z decays, the signal-to-background ratio is significantly worse, i.e. ~1:20(~1:30). This ratio can be enhanced greatly by raising the ET threshold.

If in addition to the track cuts described previously, a B-layer hit is required and |d0| < 1 mm, itis found that the number of photon conversion candidates is reduced by a factor 3 to 5, withoutcompromising the electron efficiency. However, photon conversions are not the dominant con-tribution to the background, and the reduction in their rate is discussed in the next section.

6.1.4 Further Jet Rejection

The events surviving the calorimeter and tracking selection criteria described above contributean electron rate of ~1.3 × 10-4 (~1.2 × 10-4), and a QCD-jet rejection of ~2.5 × 103 (~2.0 × 103). TheQCD-jet rejection can be improved by using the transition radiation (TR) rejection of the TRTand the removal of photon conversions by direct reconstruction. TR rejection factors corre-sponding to low luminosity have been taken from the work reported in Section 4.6, where itwas seen that the rejection is strongly |η| dependent. In Section 6.3.2, rejections of the order of10 were found for high energy conversions. In this work, a value of 15 has been used in antici-pation of greater rejection at lower energies. It is assumed that both of these rejections can beachieved with a 90% electron efficiency.

The rejection factors from these studies, together with the rates which can be attained, areshown in Tables 6-7 and 6-8. After applying these factors, the signal-to-background ratio be-

Table 6-5 Observed rates from jet sample from xKalman after different stages of selection. (See text for expla-nation of e, ‘γ ‘, and ‘h‘).

|η|

Rates (10-4)

After calo cuts After track cuts After E/p match

e ’γ ’ ’h’ e γ(e+e−) h± e γ(e+e−) h±

0.0 - 0.7 1.5 ± 0.4 51.1 ±2.2 9.7 ±0.9 1.5 ± 0.4 1.4 ± 0.4 16.9 ±1.2 1.2 ± 0.3 0.4 ± 0.2 3.2 ± 0.5

0.7 - 1.37 1.6 ± 0.4 59.6 ±2.4 16.1 ±1.3 1.7 ± 0.4 1.5 ± 0.4 23.1 ±1.5 1.5 ± 0.4 0.3 ± 0.2 4.9 ± 0.7

1.52 - 2.0 2.0 ± 0.6 63.8 ±3.2 9.3 ±1.2 1.6 ± 0.5 6.2 ± 1.0 19.1 ±1.8 1.3 ± 0.5 1.1 ± 0.4 2.6 ± 0.7

2.0 - 2.5 1.1 ± 0.4 54.2 ±3.1 5.5 ±1.0 1.1 ± 0.4 4.1 ± 0.8 12.0 ±1.5 0.9 ± 0.4 1.2 ± 0.5 1.8 ± 0.6

Table 6-6 Observed rates from jet sample from iPatRec after different stages of selection. (See text for expla-nation of e, ‘γ ‘, and ‘h‘).

|η|

Rates (10-4)

After calo cuts After track cuts After E/p match

e ’γ ’ ’h’ e γ(e+e-) h± e γ(e+e-) h±

0.0 - 0.7 1.5 ± 0.4 51.1 ±2.2 9.7 ±0.9 1.4 ± 0.4 0.9 ± 0.3 11.3 ±1.0 1.1 ± 0.3 0.7 ± 0.2 3.8 ± 0.6

0.7 - 1.37 1.6 ± 0.4 59.6 ±2.4 16.1 ±1.3 1.5 ± 0.4 0.9 ± 0.3 20.0 ±1.4 1.2 ± 0.3 0.7 ± 0.3 6.9 ± 0.8

1.52 - 2.0 2.0 ± 0.6 63.8 ±3.2 9.3 ±1.2 2.3 ± 0.6 2.0 ± 0.6 15.0 ±1.6 1.6 ± 0.5 0.7 ± 0.3 3.8 ± 0.8

2.0 - 2.5 1.1 ± 0.4 54.2 ±3.1 5.5 ±1.0 0.9 ± 0.4 3.9 ± 0.8 11.1 ±1.4 0.9 ± 0.4 1.1 ± 0.4 1.4 ± 0.5



comes ~6:1 (~5:1), with an overall electron reconstruction efficiency of ~70% (~68%), deter-mined from the electrons with pT = 20 GeV. If the electron signal is restricted to that from W andZ decays, then the signal to background ratio drops to ~ 1:1 for both reconstruction algorithms.

It should be emphasised that the above values for the electron reconstruction efficiency and jetrejection correspond to the performance of the combined calorimeter-tracker system very closeto the trigger threshold. For low luminosities, the electron efficiency of ~87% (~84%) atpT = 20 GeV increases slightly to ~89% (~84%) at pT = 40 GeV. However, if in addition, the ETcut is raised to 35 GeV, with little change to the signal efficiency, the jet rejection can be doubled(see Table 4-1 in [6-2]).

The errors quoted above for the electron efficiencies and jet rejections are purely statistical. Sys-tematic errors will arise from uncertainties in production cross-sections, jet fragmentation, thedetector model and the simulation. The overall systematic uncertainty on the expected sig-nal-to-background ratio is at least a factor of 2 if the signal is restricted to electrons from W/Zdecays and much more (i.e. a factor ~5) if electrons from b- and c-decays are included.

6.1.5 Summary

The two reconstruction programs, xKalman and iPatRec, used in the present analysis, havebeen found to give consistent results, within errors, throughout these studies for high-pT elec-trons.

Table 6-7 Observed rates from jet sample from xKalman including TR and conversion cuts. See text for expla-nation of e, γ and h.

|η|

Rejection Factors Rates (10-5)

After TR and Conversion cuts

Conversions TR e γ(e+e-) h±

0.0 - 0.7 15 14 ± 3 9.8 ± 3.1 0.25 2.3 ± 1.4

0.7 - 1.37 15 33 ± 7 12.3 ± 3.5 0.21 1.5 ± 1.2

1.52 - 2.0 15 111 ± 37 10.6 ± 4.2 0.77 0.24

2.0 - 2.5 15 42 ± 5 7.1 ± 3.6 0.83 0.43

Table 6-8 Observed rates from jet sample from iPatRec including TR and conversion cuts. See text for expla-nation of e, γ and h.

|η|

Rejection factors Rates (10-5)

After TR and Conversion cuts

Conversions TR e γ(e+e-) h±

0.0 - 0.7 15 14 ± 3 9.0 ± 2.9 0.44 2.7 ± 1.6

0.7 - 1.37 15 33 ± 7 9.8 ± 3.1 0.48 2.1 ± 1.4

1.52 - 2.0 15 111 ± 37 13.2 ± 4.6 0.44 0.34

2.0 - 2.5 15 42 ± 5 7.1 ± 3.6 0.71 0.34



Using calorimeter information alone, an overall QCD-jet rejection of ~150 has been obtained foran electron efficiency of ~98% at low luminosity. The addition of track selection and E/p match-ing to the calorimeter cluster improves this QCD-jet rejection to ~2.5 × 103 (~2.0 × 103) for anoverall electron efficiency of ~87% (~84%). This electron efficiency is |η| dependent, and is cor-related to the amount of material traversed. At this level of cuts, the residual events in the jetsample consist of electrons (mostly signal processes), photon conversions, and chargedhadrons, which occur in the ratio of approximately 2:1:4 (2:1:5). The signal-to-background is~1:3 (~1:4) for all electrons, and only ~1:20 (~1:30) for isolated electrons from W and Z decays.

Further selection cuts, exploiting partner searches to reject photon conversions and Dalitz de-cays, as well as the TR functionality of the TRT, lead to an ultimate signal-to-background of ~6:1(~5:1), for an overall electron efficiency of ~70% (~68%).

From a knowledge of the event generation level information, it is possible to associate 6 (6) elec-tron candidates to parent IVB’s and 35 (31) to b- or c-quark semileptonic decays, in the totalsample of electron candidates remaining after the E/p selection criteria. The expected numbersof electrons contained in the jet sample from IVB production are 7.9 and from b- and c-quarksemileptonic decays, 104. Therefore the observed overall identification efficiency is 76 ± 15% forelectrons from W/Z decays and 32 ± 5% from b- and c-quark semileptonic decays. The latterrepresents an average of the number found by the two track reconstruction algorithms; the er-rors are statistical.

The complete inclusive electron signal can be used for detector calibration purposes, exploitingthe E/p ratio. Additional kinematic and calorimeter information (missing transverse energy inthe case of a W boson, and detection of a second electron in the case of a Z boson) can be used toseparate the smaller signal originating from W/Z decays from the b- and c-quark semileptonicdecays.

Within the present statistical and systematic uncertainties, the inclusive electron signal fromknown processes with pT > 20 GeV can be cleanly identified at low luminosity using the fullfunctionality of the ATLAS detector. The rate of signal to background from QCD-jets is 5:1 forall electrons and 1:1 for isolated electrons from W and Z decays (before topological cuts are ap-plied).

6.2 Low-pT Electrons

6.2.1 J/ψ → e+e−

6.2.1.1 Kinematic Reconstruction of J/ψ

Low-pT electrons have been studied in the context of the decays J/ψ → e+e− and comparisonhas been made with J/ψ → μ+μ−. events were generated using PYTHIA, fullysimulated and reconstructed in the Inner Detector using the xKalman program. As described inSection 2.5.2.3, xKalman is able to perform a brem fit1 to electron candidates identified by their

1. This is the standard xKalman brem-fit and does not make use of the EM calorimeter as was done inSection 6.1

Bd0

J ψ⁄→ Ks0



transition radiation (TR) signature in the TRT. The brem fit takes into account bremsstrahlungalong the electron trajectory. Results are presented before and after the brem fit for the electrondecay of J/ψ.

Tracks with

• Number of precision hits ≥ 7,

• Number of TRT hits ≥ 9,

• pT > 0.5 GeV,

were selected and all opposite charged track pairs were fitted to a common vertex. The fit forcesthe two tracks to come from a common 3-D space-point, redefining their momenta accordingly.Successful fits with a χ2 per degree of freedom > 6 were rejected.

Figure 6-11 shows the reconstructed J/ψ peak after all cuts for muons, electrons before the bremfit and electrons after the brem fit. The distributions are given for the |η| of the J/ψ in two re-gions: |η| ≤ 0.7 and |η| > 0.7 (this does not guarantee that the leptons go into these regions).Only events for which both lepton tracks could be successfully associated with the generatedleptons enter these histograms. The peak reconstructed from the muons is Gaussian due to theeffect of detector resolution. However, the bremsstrahlung broadening of the peak for electronsis clear. It can be seen that the brem fit procedure has restored some of the symmetry of the J/ψpeak.

The central peaks of the distributions shown in Figure 6-11 have been fitted with Gaussian dis-tributions, with care to exclude the radiative tails. The fitted resolutions of the J/ψ are shown inTable 6-9.

Figure 6-11 Invariant mass distributions for a) and d) J/ψ → μ+μ−, b) and e) J/ψ → e+e− before brem fit and c)and f) J/ψ → e+e− after brem fit. Upper plots show decays in |η| ≤ 0.7; lower plots in |η| > 0.7.

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6.2.1.2 Rejection of Combinatorial Backgrounds using TR Information

In the previous section, the J/ψ invariant mass distribution was shown for pairs of tracks whichhave been identified as leptons by using the Monte Carlo truth information. For real data,things are much more complicated. The trigger will select, with reasonable purity, events whichcontain heavy flavour. However, only a fraction of these will contain the decays studied here:Br( ) = 7 × 10−4, and hence there is the potential for a huge combinatorial back-ground. To get an indication of how this background might be reduced, it has been studied justin the sample of events containing the signal itself.

Applying the same procedure, discussed inthe previous section, results in the invariantmass distribution shown in Figure 6-12(dashed line).

As explained in Section 4.6, the TRT electronidentification is based on the ratio, R, of highthreshold TR hits to all hits associated to atrack. In addition to the ratios for the individ-ual tracks (R1, R2), a combined ratio R12 isformed from the sum of the TR hits on bothtracks and the sum of all the hits on bothtracks. The cuts used were optimised for thecases where a) both electrons are in the barrel(|η| ≤ 0.7), b) neither electron is in the barreland c) where just one electron is the barrel.The cuts are shown in Table 6-10 along withthe efficiencies for the signal and the back-ground.

The invariant mass distribution after thesecuts is also shown in Figure 6-12 (solid line). Arejection factor about 20 can be achieved.Some of the remaining background includes pairs of tracks where one of the tracks is an elec-tron from the decay J/ψ → e+e−. To reduce the complete background in triggered events, an ad-ditional rejection of ~103 is required to be able to observe the signal clearly above thebackground. This can be achieved by using vertexing information.

Table 6-9 Fitted width of peak.

|η| of J/ψ Mass resolution (MeV)

J/ψ → μ+μ− J/ψ → e+e−

before brem fit J/ψ → e+e−

after brem fit

≤ 0.7 30 64 53

> 0.7 40 74 63

All 37 71 59

J ψ⁄

Bd0

J ψ⁄→ Ks0

Figure 6-12 Invariant mass distribution for all fittedtrack combinations in events containing J/ψ → e+e−

before (dashed histogram) and after (solid histogram)TR cuts.

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6.2.2 Lepton b-Tagging

The most powerful way to tag b-jets will be to look for displaced vertices - this is discussed inSection 6.7. However, the tagging of soft leptons (electrons and muons) will provide a valuablecomplement to this. In this section, the potential to tag b-jets while rejecting gluon jet back-grounds is considered in the ATLAS barrel region.

A sample of b-jets was taken from decays with mH = 100 GeV, where the b-quarks wereforced to be produced centrally and to decay to electrons (directly, or via cascades). The efficien-cy for selecting the b-jets in these events was compared with that for selecting the gluon jetsfrom . The partons (b-quarks and gluons) were required to have pT > 15 GeV and|η| < 0.3, while the electrons were required to have pT > 1 GeV and |η| < 0.6. All charged par-ticles in a cone ΔR ≤ 0.4 around the parton directions were considered (the charged multiplicityis ~6). The mean electron pT was 9.4 GeV, while the average pT of the particles in the gluon jetwas 5.0 GeV.

6.2.2.1 Track Selection and Event Analysis

In the first stage, information from the Inner Detector alone was used. Tracks were reconstruct-ed using xKalman and cuts were made on the following:

1. Number of precision hits.

2. Number of TRT hits.

3. Fraction of transition radiation hits (TR) hits - to remove hadrons.

4. Number of pixel hits, one of which must be the B-layer - to remove conversions.

In the second stage, the information from the Inner Detector was matched to that from the EMcalorimeter and cuts were made on the following:

5. Ecore/p - where p is the momentum measured in the Inner Detector and Ecore is the ener-gy measured in the EM calorimeter in the most energetic 3×3 cluster of cells containingthe cell hit by the charged track.

6. |Δη| - the difference in η measured by the tracker and the η-strips of the calorimeter (eachstrip has a width 0.003 in η).

Finally the calorimeter information itself was used and cuts were made on the following:

7. E1 - the energy measured in the first longitudinal sampling.

Table 6-10 TR cuts used to identify J/ψ → e+e− decays and the efficiencies to retain signal and background(where neither particle is an electron) combinations.

Electron topology TR cuts Efficiency (%)

Signal Background

Both in barrel R1>0.12, R2>0.12, R12>0.13 72.1 1.7

Neither in barrel R1>0.14, R2>0.14, R12>0.18 85.7 0.4

One in barrel R1>0.12, R2>0.14, R12>0.16 72.3 0.6

Combined 78.4 0.6

H bb→

H gg→



8. E3/E1 - the ratio of energy in the third and first longitudinal sampling.

9. Shower width - measured in the η-strips.

The performance of the Inner Detector and EM calorimeter depend strongly on the particle mo-mentum, and so the cuts on these quantities have been optimised separately for tracks withpT ≤ 2.5, 2.5 < pT < 5 and pT > 5 GeV.

6.2.2.2 Performance

Figure 6-13 shows the fraction of TR hits on electron tracks compared to charged particles ingluon jets, integrated over pT. Figure 6-14 shows the ratio of calorimeter energy to track mo-mentum for the two types of tracks.

Table 6-11 shows the numerical values of the cuts used for each of the three pT ranges, and thecorresponding efficiencies for electrons in b-jets and particles in gluon jets are given. The effi-ciencies are evaluated independently for each of the cuts and the results of combining all thecuts after each stage are given. Fairly tight cuts, similar to those used for vertex b-tagging (seeSection 6.7), have been used at low pT to reject background, but the cuts are relaxed for higherpT, where the calorimeter has good energy and position resolution.

The discriminating quantities discussed above have been evaluated for each charged particle inthe jet cone, and should any one particle satisfy all the cuts, the jet was accepted. The probabili-ty for the inclusive process b→eX is 17% for an electron pT > 1 GeV. Hence the b-tagging effi-ciency which can be obtained is the product of this value with the efficiencies of Table 6-11.These efficiencies, along with the rejection factors for gluon jets are given in Table 6-12. For con-sistency with the calculations of Section 6.7.8, the electrons from gluon splitting to heavy fla-vour have been removed.

Figure 6-13 Fraction of TR hits on electron track fromb-quark decay (shaded) and charged particles ingluon jets (open).

Figure 6-14 Ratio of calorimeter energy to trackmomentum for electron track from b-quark decay(shaded) and charged particles in gluon jets (open).

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6.3 Photon Identification

The decay H → γγ is a rare decay mode with a branching ratio around 1.5×10-3, however it isconsidered to be the most promising channel for a Higgs search in the mass range80 ≤ mH ≤ 130 GeV. To remove background, it is essential to verify that photon candidates reallyare photons and not electrons - this requires charged track identification. Unfortunately the verypresence of a tracker to identify these electrons leads to problems:

• Background electrons can undergo bremsstrahlung and look like signal photons.

• Signal photons can convert and look like background electrons.

Fortunately it is possible to recover to a large extent from of these problems.

Table 6-11 Efficiencies for electrons in b-jets and charged particles in gluon jets. Efficiencies are given for eachcut alone, while total (Tot.) efficiencies show effect of all preceding cuts. Where no cut is shown, no cut is made.

Cuts Efficiencies (%)

pT < 2.5 2.5 < pT < 5 5 < pT Electrons inb-jets

Particles ingluon jets

Precision hits ≥ 9 ≥ 9 97.0 ± 0.5 90.2 ± 0.3

TRT hits > 20 96.5 ± 0.5 97.2 ± 0.1

Fraction of TR hits > 0.2 > 0.16 > 0.1 84.7 ± 1.0 11.0 ± 0.3

Pixel hits (inc B-layer) ≥ 2 ≥ 2 ≥ 2 97.0 ± 0.5 88.9 ± 0.3

Tot. Inner Detector 79.3 ± 1.2 8.5 ± 0.2

Ecore/p 0.45 - 1.11 0.53 - 1.05 0.67 - 1.43 87.3 ± 1.0 54.1 ± 0.4

|Δη| (strips) < 1.8 < 1.0 90.9 ± 0.9 75.3 ± 0.4

Tot. Matching 82.0 ± 1.2 48.9 ± 0.4

Tot. ID + Matching 63.9 ± 1.5 1.2 ± 0.09

E1 (GeV) > 0.45 > 0.25 > 0.55 85.0 ± 1.1 11.5 ± 0.3

E3/E1 < 0.1 < 0.2 90.2 ± 0.9 54.5 ± 0.4

η-width (strips) < 0.85 97.9 ± 0.4 94.5 ± 0.2

Tot. Calorimeter 64.0 ± 1.5 3.5 ± 0.2

Tot. ID + Matching + Calo 50.4 ± 1.4 0.15 ± 0.03

Table 6-12 b-tagging efficiencies and gluon jet rejections for soft electron tag.

Cuts b-tag efficiency (%) Gluon jet rejection

Inner Detector only 13.5 1.9

ID + Matching 10.9 13.2

ID + Matching + Calo 8.6 105



6.3.1 Background from Electrons

For mH ≈ mZ, the background from Z → e+e− is very dangerous, since it is resonant and has across-section 25,000 times larger than H → γγ. To reduce the background to 10% of the signal re-quires an electron rejection of 500. This requires that electrons must be identified and removedwith an efficiency of 99.8%.

This study [6-8] was performed in the Inner Detector barrel (at η = 0.3) using the so-called Panellayout. Features which distinguish this layout from the current simulation are:

• One pixel layer at R = 11.5 cm, with pixels of 50 μm × 200 μm.

• Five layers of crossed strips at R = 20, 30, 40, 50 and 60 cm, with Rφ strips of pitches 50, 70,100, 100 and 100 μm and z strips with pitches 100, 150, 200, 200 and 200 μm, respectively.

The work will be repeated with the current layout over the full η range.

Photons with pT = 40 GeV and pile-up were compared to single electrons also with pT = 40 GeVwithout pile-up - a conservative approximation. It was found that about 0.15% of electrons lost95% of their energy at the first pixel layer, reducing the best achievable efficiency to about99.85%.

The procedure used in the study was:

1. Form a helical road from the EM cluster and search the first 3 layers of the Inner Detectorfor a track segment.

2. Check χ2 of track candidate, allowing one layer to be inefficient.

This provides enough rejection provided the silicon efficiency is ≥ 98%. To accommodate poorerperformance, the TRT was used:

3. Search for track in TRT near calorimeter cluster.

4. Ignore tracks with pT ≤ 5 GeV, to avoid losing too many photons due to nearby pile-uptracks.

5. Use TR discrimination.

The pT distributions for all tracks reconstructed in the TRT with pT ≥ 0.5 GeV can be seen inFigures 6-15 and 6-16. The low momentum tracks seen associated with the electrons are the re-sult of subsequent conversions of bremsstrahlung photons. The tracks associated with the pho-ton come from pile-up.



Figure 6-17 shows the electron veto efficiencywhich can be achieved as a function the pho-ton efficiency. Three different silicon efficien-cies are used, and for each a set of points isdetermined for various Rφ widths of thesearch road in the precision tracking. With thecombination of the precision layers and theTRT, provided the silicon efficiency is ≥ 95%,the required electron veto efficiency can be ob-tained with a photon efficiency ≥ 86%. Thissatisfies the specification (P4) of an electron re-jection of 500 for a photon efficiency of ≥ 85%.

Figure 6-15 pT distribution of TRT tracks near a calo-rimeter cluster associated with a pT = 40 GeV elec-tron; with (solid) and without (dashed) beamconstraint.

Figure 6-16 pT distribution of TRT tracks near a calo-rimeter cluster associated with a pT = 40 GeV photon;with (solid) and without (dashed) beam constraint.

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Figure 6-17 Electron veto efficiency vs photon effi-ciency for different silicon detector efficiencies.

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6.3.2 Recovery of Converted Photons

In the material of the Inner Detector, manyphotons will convert and the identification ofthese will be crucial for some physics studies.The distribution of conversion points in the In-ner Detector barrel is shown in Figure 6-18.

The main source of photons at LHC will below-pT photons originating from π0 decays inpile-up events. Photons with higher pT willcome from initial and final state radiation inhard scattering processes and from decays ofhigh energy π0’s in jets. These represent sourc-es of background for the decay H → γγ.

While the calorimeter will dominate in theidentification of photons, the tracker can helpin some situations. For the H → γγ decay, thecluster size can be optimised separately forconverted and non-converted photons. In ad-dition the reconstructed photon momenta inthe tracker can improve the π0/γ separation ofthe calorimeter.

For other physics channels the removal of conversions will be of interest. This includes the iden-tification of inclusive electrons (see Section 6.1) and for b-tagging, the removal of fake second-ary vertices arising from electrons in photon conversions (see Section 6.7).

6.3.2.1 Method for Conversion Identification

The identification of converted photons in the Inner Detector consist of two steps:

1. Pattern recognition to find all tracks inside a predefined cone.

2. Check if any combination of tracks are compatible with a conversion hypothesis.

A slightly modified version of the pattern recognition is needed for this work, to allow fortracks which:

• Start at radii in the volume of the tracker, rather than near R = 0.

• In general, have large impact parameters.

• Do not always have hits in the silicon detectors.

Conversions with R < 40 cm will cross at least two superlayers in the precision tracker and con-sequently, the xKalman algorithm can be used to find the tracks.

For conversions with R > 40 cm, a pattern recognition algorithm has been developed especially.It uses only the TRT and is based on a histogramming algorithm. The algorithm scans for tracksby changing the three parameters (φ,κ,Rc), where φ is the azimuthal angle at the point of closestapproach to x=0,y=0, κ is the curvature signed with the charge and Rc is the radius of conver-sion. The drift-time information from the straws in the TRT is included in the histogramming

Figure 6-18 Distribution of conversions in the InnerDetector at η = 0.3. The right-hand scale shows theintegrated fraction of all photons which convert belowa given radius.

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phase to improve the two-track resolution, which is important for separating symmetric conver-sions. However, the algorithm is not a general one for finding tracks with very large impact pa-rameter, since it only looks for tracks formed by a converted photon with its origin at theprimary vertex.

After the tracks have been found, the conversion identification can start. As a preselection, onlytracks with opposite charge and pT > 0.5 GeV are used. A χ2 fit is then made to the parametersof the two tracks with the constraints of:

• A common vertex in 3-D.

• A zero opening angle, corresponding to a massless photon.

• The reconstructed photon pointing back towards the primary vertex in the transverseplane.

The final selection of identified conversions is based on the χ2 of the constrained fit and the frac-tion of TR hits on the tracks. Both cuts filter out fake conversions from random hadron combina-tions in the pile-up. The additional rejection which is obtained from using the TR informationvaries between 3.5 at |η| = 0.5 and 21 at |η| = 2.0. This is significantly lower than might beguessed naively from Section 4.6 because of the effects of pile-up, combinatorials, elec-tron-hadron combinations and the need to retain a reasonable efficiency.

6.3.2.2 Performance

The identification of conversions has been tested mainly on a sample of photons and π0’s simu-lated with pT = 50 GeV over all η. This is close to the average pT of photons expected from trig-gered H → γγ decays.

The efficiency and fake rates for conversions are normalised to conversions with Rc < 80 cm and|zc| < 280 cm. Outside this region, the efficiency for finding conversions falls quickly to zero asthe amount of the Inner Detector crossed decreases.

The efficiency is almost flat across the Inner Detector volume, with an exception of conversionstaking place close to the transition region between the barrel and end-cap TRT. The track searchis performed down to pT = 0.5 GeV, below which tracks begin to loop, and tracks are found withhigh efficiency down to pT ≈ 1 GeV. For pT = 50 GeV photons, this leads to a loss of 2% in effi-ciency. The distributions of the efficiency for recovering converted photons are shown inFigures 6-19 and 6-20.The fall at large radii is mainly caused by conversions lost in the transi-tion region between the barrel and end-cap TRT.

The efficiency as a function of the pT of the lowest energy conversion electron pTmin is inde-

pendent of pTmin, until this gets below 1 GeV. Early conversions have a reconstruction efficiency

integrated over η of 85%. The efficiency to reconstruct the high-pT electron in this study is 95%.Hence the efficiency to identify the second conversion electron and associate it with the first,given that the high-pT electron has been identified, is 85%/0.95 = 90%. If only tracks withpT > 0.5 GeV are considered, this efficiency rises to 92%. This number can be compared with thespecification (P2) of ≥ 90%.



How well the photon is reconstructed de-pends strongly on the radius of conversion Rc.Various reconstructed parameters (integratedover all η) are summarised in Table 6-13. Re-constructed momentum distributions after thefit are shown in Figure 6-21. A brem fit, in-cluding the position of the electromagneticcluster, is not possible for conversions andhence it is not possible to reduce the large tailfrom bremsstrahlung.

Total efficiencies for finding reconstructedconversions are meaningful only when a com-parison is made with the number of fake con-versions identified in the presence of pile-up.Fake conversions arise mainly from pairs ofuncorrelated charged pions, and it is desirablethat this rate should be well below the rate ofreal conversions from π0 decays from thepile-up.

The strongest handle to reject fake conversions is the number of TR hits on the tracks. This is es-pecially true for tracks crossing the end-cap TRT, where the TR yield is higher than in the barrelTRT. The rate of fake conversions is defined as the rate of conversion candidates in pile-upevents at full luminosity where true conversions in the pile-up have been subtracted. Rates arenormalised to a road size of Δη×Δφ = 0.2×0.2 and are shown in Table 6-14.

Figure 6-19 Efficiency for reconstructing convertedphotons with pT = 50 GeV as a function of the conver-sion radius Rc.

Figure 6-20 Efficiency for reconstructing convertedphotons with pT = 50 GeV as a function of |η| of thephoton.

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6.3.2.3 π0 Rejection

To reduce the background from jet-jet and jet-γ combinations to the H → γγ signal, it is necessaryto provide a rejection of π0’s on top of the jet rejection provided by the calorimeter. The algo-rithm for this is based on the shower shape in the η-strips of the calorimeter [6-2]. If a primaryphoton has converted, the shower gets slightly broader even in the non-bending plane, and theπ0 rejection falls below a factor 3 at a fixed photon efficiency of 90%. This degradation in π0 re-jection can be more than regained by including the tracker information.

If a primary photon converts, the reconstructed transverse momentum in the tracker is close tothe transverse energy in the corresponding EM cluster. However, for a highly energetic π0 witha converted photon, the reconstructed transverse momentum of the photon pT

1+pT2 generally

will be below the total energy in the cluster ET, which includes energy from the conversion plusthe unconverted photon. The ratio of these two is shown in Figure 6-22. It can be used to dis-criminate between photons and π0’s: for photons, the ratio is peaked at 1, with an r.m.s. whichreflects the resolution; for π0’s, the ratio is fairly flat between 0 and 1, representing the energysharing between the two photons in the π0 decay.

The rejection which can be achieved against π0’s is illustrated in Figure 6-23. For a 90% photonefficiency, it is possible to achieve a π0 rejection of 2.4

The use of the Inner Detector without information from the η-strips of the calorimeter is notvery efficient and a combined method for π0 rejection is necessary. As a first step in a combinedanalysis all photon candidates with an identified conversion were selected. This is done with anaverage efficiency across the Inner Detector of 85%.

For early conversions, the pT resolution of the conversions is good and gives the dominant re-jection for π0’s; while for later conversions, the essential information provided by the Inner De-tector is that a conversion has taken place.

a. Refers to tails in pT distribution after fit and corresponds to previous column.

Table 6-13 Reconstructed parameters for photon conversions.

Rc(cm)

σ(pT)/pTbefore fit

σ(pT)/pTafter fit

Tailsa

outside ±2σσ(Rc)(cm)

σ(φ0)(mrad)

σ(z0)(cm)

0 - 20 0.051 0.040 0.46 0.88 0.17 0.03

20 - 40 0.17 0.14 0.20 1.03 0.10 0.54

40 - 60 0.31 0.23 0.15 4.09 0.96 -

60 - 80 0.28 0.23 0.09 4.29 1.16 -

Table 6-14 Efficiencies and fake rates for conversions.

|η| Efficiency Rate in pile-up Fake rate

0.0 - 0.6 0.87 2.3×10-3 5.7×10-3

0.6 - 1.2 0.70 2.8×10-3 12.1×10-3

1.2 - 1.8 0.85 4.5×10-3 < 0.7×10-3

1.8 - 2.4 0.85 3.3×10-3 9.5×10-3



Based on the reconstructed conversion radius and η, the data are divided into subsamples. Theπ0 rejection is optimised in each subsample keeping the efficiency for identified conversions inthe photon sample at 90%. Results are summarised in Tables 6-15 and 6-16.

Figure 6-22 Ratio of reconstructed conversion pT tototal cluster ET for photons and π0’s at low luminosity.

Figure 6-23 π0 efficiency as a function of photon effi-ciency for different cuts on (pT

1+pT2)/ET.

Table 6-15 π0 rejection (for fixed efficiency of 90% to reconstruct photon conversions) as a function of conver-sion radius. Also given is the fraction of photons which convert in each interval.

Rc (cm) π0 efficiency (%) Conversion fraction (%)

0 - 20 16 5.8

20 - 40 30 4.8

40 - 60 32 5.6

60 - 80 37 4.6

0 - 80 29 20.8

Table 6-16 π0 rejection (for fixed efficiency of 90% to reconstruct photon conversions) as a function of |η|. Alsogiven is the fraction of photons which convert in each interval.

|η| π0 efficiency (%) Conversion fraction (%)

0.0 - 0.6 20 3.8

0.6 - 1.2 16 6.0

1.2 - 1.8 35 4.2

1.8 - 2.4 36 6.9

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1

0.5 0.6 0.7 0.8 0.9 1



For conversions in the Inner Detector barrel, a π0 rejection of 5 can be achieved, which is betterthan the rejection for unconverted photons seen by the EM calorimeter [6-2]. Over the fullη range, with identified conversions, the mean efficiency for identifying a π0 as a photon is 0.29,with a photon efficiency of 90%.

6.4 Primary Vertex Reconstruction

In this section, the reconstruction of the primary vertex on an event by event basis is discussed.This study has been performed using various datasets for which the knowledge of the primaryvertex position is crucial for the physics. The standard simulation of the collision point has beenused, as described in Section 2.4: σx = σy = 15 μm and σz = 5.6 cm. The uncertainty on the vertexposition given by the beam envelope is already very good in the transverse plane; but clearly, inthe z direction, it is necessary to measure the vertex position.

xKalman has been used to reconstruct tracks in the complete event which satisfy:


• Number of TRT hits ≥ 9.

• pT > 0.5 GeV.

Further track quality cuts are applied:

• Number of pixel hits ≥ 2.

• At least one associated hit in the B-layer.

• χ2 per degree of freedom < 6.

All selected tracks are fitted to a common 3-Dvertex. This fit is totally unguided and doesnot rely on the event topology in any way, andso it can be applied to virtually any samplewith only minor changes to the cuts. A χ2 isformed and the track which makes the maxi-mum contribution is identified and removed ifits contribution exceeds some value ξ (themaximum χ2 contribution). The process is iterat-ed until no further tracks are removed or lessthan two tracks are left. With this algorithm, itis possible to remove mismeasured tracks,tracks coming from secondary decay verticesand tracks coming from interactions. Due tothe large number of tracks entering the fit, it isfound that the results depend little on thetrack cuts, but there is a strong dependence onthe value of ξ.

If the cut on ξ is too loose, poor tracks enterthe vertex fit and the resolutions degrade andthe width of the pulls increase. If the cut is tootight, genuine primary tracks are removed and

Figure 6-24 z resolution of primary vertex andnumber of tracks used in fit as a function of ξ, the max-imum χ2 contribution allowed for any track, for

.

0 12 24 36 48 6040

44

48

52

56

60

13

14

15

16

17

18

z R

esol

utio

n (μ

m) Fitted T

racks

Max. χ2 Contribution

z resolutionFitted tracks

Bd0

J ψ⁄ K s0→



statistical precision is lost. For each different event sample, the cut has been optimised to givethe best resolution. The variation in z resolution which can be achieved as a function of the val-ue of ξ is shown in Figure 6-24 for events containing the decay . A clear mini-mum in the resolution distribution is seen for ξ around 7.5.

The performance of this algorithm for various samples is summarised in Table 6-17. The preci-sion of the vertex position depends mainly on the number of tracks successfully fitted. The bestresults from the samples examined, are obtained from the sample, where the resolu-tions are 11 μm in the transverse plane (smaller than the beam spot size) and 24 μm along thebeam line. These values almost double for the B samples and for the sample, for whichthe residuals in x and z are shown in Figures 6-25 and 6-26. The results for minimum bias eventsare dominated by the low charge multiplicity (pT > 0.5 GeV); hence the resolutions worsen to50 μm in the transverse plane and 70 μm along the beam line. This is well within the specifica-tion (B5) that σ(z) should be < 1 mm.

a. all refers to all reconstructed tracks; good refers to tracks satisfying all quality cuts; fitted refers to trackssurviving the iteration procedure and used in the vertex fit.

Table 6-17 Summary of primary vertex finding results on various samples.

Sample Tracks(all/good/fitted)a

σx (μm) σy (μm) σz (μm)

Single min. bias 15.8/10.8/10.2 47 48 70

,mH=100 26.0/17.1/15.9 26 26 44

,mH=400 60.2/43.3/35.8 10 11 24

31.6/22.0/17.9 29 27 44

31.6/22.8/17.8 29 29 47

Figure 6-25 Residuals on x measurement of primaryvertex for .

Figure 6-26 Residuals on z measurement of primaryvertex for .

Bd0

J ψ⁄→ Ks0

H bb→

H γγ→

H γγ→

H bb→

B J ψ⁄ K→

Bs Ds π→

0

100

200

300

-0.02 -0.01 0 0.01 0.02

x Residuals (cm)

0

100

200

-0.02 -0.01 0 0.01 0.02

z Residuals (cm)

H γγ→ H γγ→



6.5 V0 Reconstruction

The reconstruction of long-lived particles, such as and Λ, is crucial in order to be able to re-construct rare B-meson decay channels. In this section the decays → π+π− and Λ → pπ− areconsidered. It is also likely to be important in b-tagging, since the daughters of V0’s tend to havelarge impact parameters, yet in some cases not so large that then can be trivially removed by acut on d0. If the V0 can be reconstructed, the impact parameter of the V0 itself can be used.

Two potential problems are anticipated for the reconstruction of V0’s. Firstly, the pT spectrum ofV0’s generated in the physics processes of interest (i.e. B-decays) is quite soft - the mean is6 GeV. Consequently, the decay products tend to have low pT, close to the point aroundpT ≈ 0.5 GeV, below which the pattern recognition algorithms become inefficient. Secondly, forthose V0’s which have a larger boost, the decay may take place in the volume of the Inner Detec-tor, causing an absence of hits at low radii. Further, such tracks will tend to have large impactparameters when the tracks are extrapolated back towards the primary vertex, and this may beproblematic, since the pattern recognition algorithms are designed primarily to find tracks orig-inating from close to the primary vertex.

Such studies [6-9][6-10] were first performed using the old Cosener’s layout [6-11]. It turns outthat the performance obtained for that layout was better due to the precision layers at high ra-dii. However, the work presented here represents an improved simulation, which includes ma-terial interactions and a more realistic description of detector noises and inefficiencies. Thetracking algorithm used is more sophisticated, allowing the full rapidity range up to |η| ≤ 2.5to be considered.

6.5.1 Description of the V0 Finding Algorithm

The V0 finding algorithm uses charged tracks reconstructed by xKalman, since there may bemissing hits on the inner layers, and so it is essential to start from the TRT. By varying the mini-mum number of precision layer hits to be included in the track fit, reasonable efficiencies forlong-lived V0’s can be achieved. In what follows, a minimum of four precision hits on a trackhas been required. In the barrel region, this permits V0’s to be reconstructed with decay radii upto 44 cm.

Only tracks with pT ≥ 0.5 GeV are used and V0 candidates are obtained by first fitting pairs ofoppositely charged tracks to a common vertex. Pairs for which the χ2 per DoF is ≤ 6 are re-tained. To reduce further the background, we require that the reconstructed decay vertex beseparated by ≥ 1 cm from the beam axis. For candidates, pion masses are assigned to bothtracks and the invariant mass of the pair is computed with the momenta recalculated by the fit.Likewise, for the Λ search, proton and pion masses are assigned to the two tracks, with the hy-pothesis that the highest pT track is the proton. Finally, all track pairs lying within a 20(10) MeVwindow around the nominal (Λ) mass are treated as (Λ) candidates.

Ks0

Ks0

Ks0

Ks0

Ks0



6.5.2 Performance for Single V0 Events

The performance of the algorithm described above has been checked on samples of and Λgenerated at various fixed pT (3, 5 and 7 GeV), characteristic of B-decays. The reconstruction ef-ficiency is defined as the ratio of the number of events which pass all selection cuts to the totalnumber of Monte Carlo events having a and two pions with pT ≥ 0.5 GeV and |η| ≤ 2.5,with a decay radius between 1 and 44 cm. A similar definition is used in the Λ case.

In Figures 6-27 to 6-33, efficiencies and resolutions are shown. Statistical error bars are shownonly for the measurements for pT = 3 GeV, but are similar for the other curves. The dotted anddashed lines are solely to guide the eye. In Figures 6-27 and 6-28, the reconstruction efficienciesfor ’s and Λ’s are shown as a function of decay radius. For decays which occur before the firstSCT layers (Rdecay < 30 cm), the average reconstruction efficiency is around 75%, while forΛ’s it is around 70%.

Generally, the distributions for the two V0’s are quite similar, and therefore will be shown main-ly for ‘s. Figure 6-29 shows how the efficiency varies with |η|. The performance is reducedin the region of the overlap between the barrel and end-cap regions. From Figure 6-30, it can beseen that, for the range of V0 pT’s which can be expected, the efficiency does not depend on theV0 momentum. It is found that the reconstruction efficiencies are not too sensitive to the maxi-mum impact parameter |d0| of the two decay products, up to about 4 cm; but beyond this, theefficiencies fall.

Figure 6-27 Efficiency for reconstruction as afunction of decay radius.

Figure 6-28 Efficiency for Λ reconstruction as a func-tion of decay radius.

Ks0

Ks0

Ks0

Ks0

0

0.25

0.5

0.75

1

0 10 20 30 40

Decay Radius (cm)

Eff

icie

ncy

K0s pT = 3 GeV

K0s pT = 5 GeV

K0s pT = 7 GeV

0

0.25

0.5

0.75

1

0 10 20 30 40

Λ pT = 3 GeVΛ pT = 5 GeV

Decay Radius (cm)

Eff

icie

ncy

Λ pT = 7 GeV

Ks0

Ks0



The resolution on the decay vertex, is shownin Figure 6-31. At low radii, where more infor-mation from the precision layers is available,the resolution is about 450 (680) μm for the(Λ) decay. The effect of the location of the de-cay relative to the precision layers (for thosedecays in the barrel) can be seen as dips wherethe resolution improves. This is most signifi-cant for the first bin, where the decays are be-fore the B-layer. The resolution is fairlyconstant as a function of the pT of the V0.Figures 6-32 and 6-33 show the mass resolu-tions of the reconstructed V0’s, again fairlyconstant as a function of pT. The resolutionsfor early decays are about 5 and 2.5 MeV for

’s and Λ’s, respectively.

Figure 6-29 Efficiency for reconstruction as afunction of |η|, for pT = 3 GeV.

Figure 6-30 Efficiency for reconstruction as afunction of pT.

0 0.5 1 1.5 2 2.50.6

0.7

0.8

0.9

1

|η| of K0s

Eff

icie

ncy

0.5

0.6

0.7

0.8

3 4 5 6 7

pT of K0s (GeV)

Eff

icie

ncy

Ks0

Ks0

Ks0

Ks0

Figure 6-31 Resolution of decay radius as afunction of that radius for all η, for pT = 3 GeV.

0

0.5

1

1.5

10 20 30 40

Decay Radius (cm)

Res

olut

ion

of D

ecay

Rad

ius

(mm

)

Ks0

Ks0

Ks0



6.6 Reconstruction of Exclusive B-decays

6.6.1 Reconstruction of Bd0 → J/ψ Ks

0 Events

The decay to a J/ψ and meson is a clean channel for measuring sin2β for CP-violationstudies. An event display containing this decay is shown in Colour Figure 2-i. The event sam-ples are identical to those in Section 6.2.1 and the J/ψ reconstruction of the tracks associatedwith the true leptons has been used, including the brem fit for the electron events.

J/ψ candidates were required to be inside a [−3σ,+3σ] mass window around the nominal massfor the muon events and inside [−nσ,+3σ] (where n is between 5 and 7, depending on the topol-ogy) for the electron events. The mass resolution σ is determined separately for the barrel(|η| ≤ 0.7) and overlap and end-cap (|η| > 0.7) regions.

Figure 6-32 Mass resolution for reconstruction asa function of decay radius.

Figure 6-33 Mass resolution for Λ reconstruction as afunction of its decay radius.

0

2.5

5

7.5

10

10 20 30 40

Decay Radius (cm)

Mas

s re

solu

tion

(MeV

)

K0s pT = 3 GeV

K0s pT = 5 GeV

K0s pT = 7 GeV

0

2.5

5

7.5

10

10 20 30 40

Λ pT = 3 GeVΛ pT = 5 GeV

Decay Radius (cm)

Mas

s re

solu

tion

(MeV

)

Λ pT = 7 GeV

Ks0

Bd0

Ks0



For all events in which a J/ψ was successfullyreconstructed, a search was made for acandidate using the algorithm described inSection 6.7. The reconstructed invariant masspeak is shown in Figure 6-34. The width of thisdistribution is about 5 MeV. All pairs within20 MeV of the nominal mass were consideredas candidates.

A global kinematical 3-D fit was performed onthe J/ψ- system: vertex and mass con-straints were applied to both the J/ψ andvertices. Also the momentum vector wasconstrained to point to the J/ψ vertex and thereconstructed B momentum vector to the pri-mary vertex. The B-meson invariant mass dis-tributions are shown in Figures 6-35 and 6-36.The B mass resolutions are given in Table 6-18.

Figure 6-35 invariant mass distribution forwith J/ψ → μ+μ−.

Figure 6-36 invariant mass distribution forwith J/ψ → e+e−.

Table 6-18 B mass resolution for the decay .

|η| of J/ψ B mass resolution (MeV)

J/ψ → μ+μ− J/ψ → e+e−

≤ 0.7 16 21

> 0.7 21 30

All 19 26

Figure 6-34 Invariant mass of reconstructed in events.

0

250

500

750

1000

0.46 0.48 0.5 0.52

Mass (GeV)

Ks0

Bd0

J ψ⁄→ Ks0

Ks0

Ks0

Ks0

Ks0

Ks0

0

20

40

60

80

5 5.1 5.2 5.3 5.4 5.5

Mass (GeV)

0

100

200

300

5 5.1 5.2 5.3 5.4 5.5

Mass (GeV)

Bd0

Bd0

J ψ⁄→ Ks0

Bd0

Bd0

J ψ⁄→ Ks0

Bd0

J ψ⁄→ Ks0



Finally, the decay positions of candidate B-mesons which fall inside a [−3σ,+3σ] mass windowaround the nominal mass were determined. The differences between the reconstructed and thegenerated decay radii for both the muon and the electron decay channels are shown inFigures 6-37 and 6-38. Gaussian fits to these distributions yield resolutions of 64 μm for themuon events and 68 μm for the electron events.

6.6.2 Reconstruction of Bs0 → Ds

− π+ Events

The decay chain is a promising channel for measuring xs, themixing parameter in the system. A time-dependent mixing measurement like this relies onthe secondary vertex resolution achievable on the . In this section, the details and difficultiesof reconstructing this decay are not considered. Instead it is demonstrated that the Inner Detec-tor can reconstruct this decay with an acceptable resolution.

Events containing the desired decays of have been generated with PYTHIA. The sample hasbeen fully simulated and the reconstruction of charged tracks has been performed using xKa-lman with default cuts. The analysis starts by looping on all opposite charge track combinationswhich were fitted with a φ resonance hypothesis by assigning the kaon mass to both particles.After a fit χ2 cut has been applied, the invariant mass of the pair was determined. This spectrumis shown in Figure 6-39 (for tracks which can be matched to the generated kaons). Although thedistribution is the sum of events with different resolutions arising from different topologies, thecentre of the peak can be fitted with a Gaussian which has a width of 3.2 MeV. All combinationslying within 3σ of the nominal φ mass were considered as φ candidates. For these candidates, anattempt was made to find a third track coming from the same vertex. This was done by loopingover all other tracks in the event and refitting the three track vertex with a pion mass assign-ment for the third track; the pion and both kaons were required to have pT > 1 GeV. The result-ing invariant mass distribution after a χ2 cut is shown in Figure 6-40. The peak has aGaussian width of 14 MeV.

Figure 6-37 Residual distribution for decay radius for

decay with J/ψ → μ+μ−.

Figure 6-38 Residual distribution for decay radius for

decay with J/ψ → e+e−.

0

10

20

30

40

-0.04 -0.02 0 0.02 0.04

Decay Radius Residuals (cm)

0

50

100

150

-0.04 -0.02 0 0.02 0.04


Bd0

Bd0

Bs0

Ds+− π± φπ−π+

K+

K−π−π+→ → →

Bs0

Bs0

Bs0

Ds−



Starting from the tertiary decay vertex, afourth track was added in an attempt to recon-struct the secondary vertex. This trackshould have the opposite sign with respect tothe pion from the and also was assigned apion mass. Only candidates falling into a3σ window around the nominal D mesonmass were considered. The reconstructed ,candidate and the pion (pT > 0.5 GeV) wereconstrained to come from a common second-ary vertex, with the additional requirementthat the total momentum at the vertex pointedto the primary vertex. Mass constraints wereimposed on the two kaons corresponding tothe nominal φ mass and on the K-K-π systemcorresponding to the mass. The resultinginvariant mass is shown in Figure 6-41 (fortracks having the right match with the gener-ated particles). A Gaussian fit to the distribu-tion gives a width of 40 MeV.

The transverse decay radius for all events within 3σ around the nominal B-meson mass hasbeen calculated and compared to the generated one. The resolution (illustrated in Figure 6-42) isabout 58 μm, however, the residual distribution has non-Gaussian tails. Figure 6-43 shows theresiduals on the proper time1, which has a Gaussian width (of peak) of about 0.073 ps.

1. The proper time is calculated in the transverse plane as LxyMinv/pT, where Lxy is the transverse de-cay-length.

Figure 6-39 Invariant mass of the K-K system. Gaus-sian fit to peak gives 3.2 MeV.

Figure 6-40 Invariant mass after the three track ver-tex fit for the K-K-π system. Gaussian fit to peak gives14 MeV.

0

200

400

600

800

1 1.01 1.02 1.03 1.04

Invariant mass (GeV)

0

200

400

1.8 1.9 2 2.1


Figure 6-41 Invariant mass spectrum of the D-π sys-tem. Gaussian fit to peak gives 40 MeV.

0

100

200

5.2 5.3 5.4 5.5


Ds+−

Bs0

Ds+−

Ds+−

Ds+−

Ds+−

Bs0

Bs0



6.7 Vertex b-Tagging

In this section, the tagging of b-quarks from the decay (mH = 400 GeV) is discussed andcompared with the rejection of lighter quark and gluon decays of the Higgs. More details aboutthe physics of these events is given in Section 2.4.3.

b-hadrons have relatively long lifetimes (cτ ≈ 460 μm). This gives rise to displaced verticeswhich may be tagged by either explicitly reconstructing the vertex or by examining the impactparameters of the daughters. In the work described in this section, the latter has been used sincefor Higgs physics, high b-tagging efficiency (rather than high purity) is required (seeSection 6.7.8). The rejection of non b-jets depends on the fact that for light quarks, most of thestable particles which can be reconstructed in the Inner Detector come from the decays ofshort-lived objects and hence appear to come from the primary vertex. The extent to which thisis true is determined by the impact parameter1 resolution σ(d0) of the detector.

1. Unless stated, impact parameter will refer to the transverse impact parameter d0, since this is the mostimportant for b-tagging.

Figure 6-42 Residual distribution for decay radius forthe reconstructed B-meson vertex. Gaussian fit topeak gives 58 μm.

Figure 6-43 Residual distribution for proper time (seetext) for the B-meson vertex. Gaussian fit to peakgives 0.073 ps.

0

200

400

-0.04 -0.02 0 0.02 0.04


0

100

200

300

400

-0.4 -0.2 0 0.2 0.4

Proper Time Residuals (ps)

H bb→



Figure 6-44 shows the impact parameter reso-lution for primary pions in jets. The rise with|η| is mainly due to the increase in materialin the forward direction. The difference be-tween iPatRec and xKalman1 arises fromthe different pixel clustering used by the twoalgorithms, as explained in Section 4.4. Theimpact of this on the b-tagging performance isdiscussed in Section 6.7.3.

Signed impact parameterWhat is of interest for b-tagging is the signedimpact parameter (sign×|d0|), where the signis positive if the track appears to originatefrom in front of the primary vertex (i.e. trackcrosses jet-axis in front of primary vertex) andnegative if it appears to originate from behind.The jet-axis will be determined accuratelyfrom the calorimeter, and since this has notbeen included in the simulation, the jet-axiswas taken as the b-quark direction.

Primary vertexIn principle, the primary vertex can be recon-structed from prompt tracks in the event, asdescribed in Section 6.4. In practice, since thegain is small, this may not be done (there is adanger of introducing systematics), and herethe impact parameter has been determinedwith respect to the nominal beam position(x = 0, y = 0 in this simulation), which is antici-pated to remain quite stable over the durationof a fill. Therefore the uncertainty on the im-pact parameter is the combination of themeasurement error σ(d0) and the spread of thebeam-spot, 15 μm, taken in quadrature. Theeffect of this is to increase σ(d0) by about 4 μm.

Significance distributionThe significance of the impact parameter is de-fined as the ratio of the signed impact parame-ter to its total error. This is shown inFigure 6-45 for tracks from b and u-jets. Bothdistributions have significant ‘cores’ whichrepresent correctly reconstructed tracks coming from the primary vertex. These cores can be de-scribed by Gaussians of width close to 1. The b-jets contain tracks with large positive signifi-cance, corresponding to genuine lifetime content. By contrast, u-jets have only a small excess oftracks which appear to contain lifetime arising from:

1. The version of xKalman used for this work used an older version of the clustering which results in apoorer impact parameter resolution than was showed in Section 4.4

Figure 6-44 Impact parameter resolution for tracksfound in b-jets from with mH = 400 GeV.

0

10

20

30

40

50

0 0.5 1 1.5 2 2.5

|η|σ(

d 0) (

μm)

xKalman 3< pT <6 GeV

iPatRec 3< pT <6 GeV

xKalman pT >10 GeV

iPatRec pT >10 GeV

H bb→

Figure 6-45 Significance distribution: signed impactparameter divided by its error. Curves for b and u-jetsare normalised to the same area.

10-4

10-3

10-2

10-1

-20 -10 0 10 20

Significance

b-jet tracks

u-jet tracks



• daughters of V0’s,

• daughters of heavy quarks formed in the fragmentation,

• interactions with material, e.g. photons converting to e+e− pairs or pions having nuclearinteractions.

There are tails in the impact parameter distributions which are apparent on the negative side ofthe significance distribution. For the b-jets, these come mainly from an incorrect determinationof the sign (corresponding to the uncertainty in determining the b-hadron direction) and com-plications arising from secondary decays of charmed states. For the u-jets, the tail is dominatedby secondaries.

6.7.1 Methods

Various methods have been used by ATLAS in the past to study b-tagging:

• Track counting [6-13] - simply count the number of tracks with significance > +3 and|d0| < 1 mm.

• ALEPH method [6-12] - invokes the probability for all the tracks in jet to come from pri-mary vertex.

• Likelihood ratio [6-13] - described below.

In the work which follows, it is the likelihood ratio method which has been used, since it ap-pears to offer the best performance.

The emphasis of these studies is on individual jets, rather than complete events. Throughout,the rejection R for different background jets is compared with the efficiency εb for keeping b-jets.The rejection is simply the reciprocal of the efficiency. If there is no discrimination at all, R willbehave like 1/ εb.

Likelihood ratio method

1. For each selected track i in a jet, the significance Si is calculated.

2. The ratio of the distributions of the significance for b-jets and u-jets is computed:ri = fb(Si)/fu(Si).

3. A jet weight is constructed from the sum of the logarithms of the ratios: W = Σ log ri.

4. By keeping jets above some value of W (a value which can be varied), the efficiency fordifferent jet samples can be obtained.

By using the significance distribution fu(S) for u-jets, the method is optimised for the rejection ofu-jets. With real data, since the jet type will not a priori be known, the rejection will have to beoptimised for each specific background under study.

6.7.2 Track Selection

Track finding was performed with xKalman over the complete event and in restricted cones foriPatRec. Only tracks with pT > 1 GeV and in a cone of ΔR < 0.4 around the jet direction wereconsidered. The following cuts were made:



• Number of precision hits ≥ 9 (no explicit TRT requirement was made, although the validdrift-time hits were used for the global track fit).

• Number of pixel hits ≥ 2.

To remove secondaries and daughters of V0’s and to improve the quality of the impact parame-ter information, further cuts were imposed:

• There must be a B-layer hit.

• |d0| < 1 mm.

After all these cuts, xKalman and iPatRec obtain similar track finding efficiencies of 86% and88% respectively for tracks from the primary vertex.

6.7.3 Basic Performance

The jet weights calculated with the likelihoodratio method are shown for u and b-jets inFigure 6-46. For mH = 400 GeV, 6% of the jetshave < 2 selected tracks and are rejected(hence do not appear in the plot) and contrib-ute directly to the inefficiency.

Figures 6-47 and 6-48 show the rejection ob-tained for u-jets. This is limited by the tail ofthe impact parameter distribution for theu-jets, which was visible in Figure 6-45. An at-tempt has been made to understand the effectsof various contributions to the tail by remov-ing certain tracks, using the Monte Carlo in-formation. The results are visible in theimproved rejection curves also shown inFigures 6-47 and 6-48. The rejections which becan be obtained for εb = 50% are summarised in Table 6-19.

From the values of Table 6-19, the following background compositions can be deduced for xKa-lman (iPatRec) respectively:

• 50% (52%) of tracks arise from interaction in the material of the detector (mainly electronsfrom photon conversions, but also nuclear interactions).

• 35% (41%) of tracks are produced in the decays of hadrons with significant lifetime (main-ly ); b and c-hadrons are produced in 1.7% of u-jets.

• 15% (7%) of tracks are produced at the primary vertex (with large deflections from multi-ple scattering or possibly pattern recognition problems).

Figures 6-49 and 6-50 show the rejections obtained for different jet types. The offset from εb = 1arises from the 6% loss of jets where there are insufficient selected tracks. The rejections forεb = 50% are shown in Table 6-20.

Figure 6-46 Jet weights from likelihood ratio.

0

0.05

0.1

0.15

0.2

-10 0 10 20

Jet Weight

Eve

nts

b-jets

u-jets

Ks0



Figure 6-47 u-jet rejection as a function of b-jet effi-ciency, including the results of removing successivelysecondaries, then tracks with large impact parameter,using the Monte Carlo information (xKalman).

Figure 6-48 u-jet rejection as a function of b-jet effi-ciency, including the results of removing successivelysecondaries, then tracks with large impact parameter,using the Monte Carlo information (iPatRec).

Table 6-19 Rejection of u-jets after various Monte Carlo ‘improvements.’

Conditions Ru for εb = 50%

xKalman iPatRec

All tracks 50 ± 3 66 ± 3

Secondary tracks excluded 102 ± 9 137 ± 8

Only prompt tracks from primary vertex 340 ± 50 920 ± 150

Figure 6-49 Background rejections as a function ofb-jet efficiency (xKalman).

Figure 6-50 Background rejections as a function ofb-jet efficiency (iPatRec).

1

10

10 2

10 3

0.2 0.4 0.6 0.8 1

εb

Ru

all trackssecondaries excludedonly prompt tracks

1

10

10 2

10 3

0.2 0.4 0.6 0.8 1

εb

Ru

all trackssecondaries excludedonly prompt tracks

1

10

10 2

10 3

0.2 0.4 0.6 0.8 1

εb

R

u-jetg-jetc-jet

1

10

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10 3

0.2 0.4 0.6 0.8 1

εb

Ru

u-jetg-jetc-jet



The rejection of c-jets Rc is not very good because of the lifetime of the c-hadrons: for D±,cτ = 317 μm; for D0, cτ = 124 μm. The rejection of gluons Rg is limited by the gluon-splitting:Br( ) = 6% and Br( ) = 4%, for mH = 400 GeV. Even if all light quarks were rejected,the gluon splitting restricts the rejection to about 30.

The rejections as a function of |η| are shown in Figures 6-51 and 6-52. The drop in rejection ob-served for 1.5 < |η| < 2.0 (compared to η ~ 0) is related to the increase of material in this region.For xKalman, in this interval, if the secondaries are removed, Ru increases from 35 to 70. Thisrejection can be compared with that obtained by degrading the impact parameter resolution atη ~ 0 to be the same as that in the interval 1.5 < |η| < 2.0. In which case, Ru falls from 90 to 70.

It is believed that the difference in performance of xKalman and iPatRec comes from the in-ternal cuts embedded in the programs, along with the different impact parameter resolutions.Since these cuts are fundamental components of the programs, it is not easy to study this. How-ever, to gain some insight, the following two cuts have been applied to the tracks from xKa-lman:

• Fit χ2 per degree of freedom < 3 (applied internally in iPatRec).

• No missing hits in two consecutive superlayers (corresponding to cut on number of holesby iPatRec).

Table 6-20 Rejections of various types of background jets.

Background jet Ru for εb = 50%

xKalman iPatRec

u-jet 50 ± 3 66 ± 3

gluon jet 26 ± 2 29 ± 1

c-jet 8.7 ± 0.4 10.2 ± 0.2

Figure 6-51 Background rejections as a function of|η| for εb = 50% (xKalman).

Figure 6-52 Background rejections as a function of|η| for εb = 50% (iPatRec).

g cc→ g bb→

1

10

10 2

10 3

0 0.5 1 1.5 2 2.5

|η|

R

u-jetg-jetc-jet

1

10

10 2

10 3

0 0.5 1 1.5 2 2.5

|η|

R

u-jetg-jetc-jet



In addition, the impact parameters from iPa-tRec have been smeared to account for thedifferences which were shown in Figure 6-44.With these modifications, Figure 6-53 showsthe u-jet rejection for two cases: a) all trackspresent (default case) and b) secondary tracksremoved. Integrating over η, the rejectionsfrom xKalman and iPatRec are both 60 ± 3,and if the secondaries are removed, thesenumbers become 108 ± 9 and 121 ± 7 respec-tively.

These results demonstrate that the two algo-rithms are capable of providing the same per-formance. It is not clear whether the operatingconditions of the real detector will permit theapplication of the additional cuts (internal orexternal) indicated above. Therefore the analy-sis using xKalman has not been modified toinclude these cuts, but rather can be consid-ered to provide a more conservative estimateof the b-tagging performance.

6.7.4 Possible Improvements

From the work presented in this section on b-tagging, it is clear that secondaries represent themost important component of the background (more than 50% for both xKalman and iPa-tRec). More than 90% of these secondaries are electrons from conversions and these could beremoved by direct tagging or indirectly by imposing quality cuts on the tracks.

Direct Tagging of ConversionsAn estimate has been made of the improvement which could be obtained by removing recon-structed e+e− pairs (along the lines described in Section 6.3.2). In xKalman, all pairs where bothelectrons were reconstructed were removed. This reduced the fraction of secondaries from 1.8%to 1.0%. The removal of the conversions may be enhanced by using electron identification withthe TRT and/or the EM calorimeter.

Quality Cuts to Remove SecondariesThere are various quality cuts which could be used to reduce the fraction of secondaries. Thefollowing have been tried:

a. Fit χ2 probability > 1%.

b. |(z0-zv) sinθ| < 1.5 mm, where zv is the z-position of the primary vertex, takenfrom Monte Carlo information and smeared by 30 μm to account for the expectedvertex resolution (see Section 6.4).

c. Number of hits shared by tracks in pixels and SCT < 2 and < 3 respectively, and nomissing hits in two consecutive superlayers.

Cut (a) is particularly successful for iPatRec: secondaries are reduced to 1.4% with a fall intrack finding efficiency from 88% to 86%. For xKalman, this cut is less useful due to the large

Figure 6-53 u-jet rejection as a function of |η| aftersmearing the impact parameter from iPatRec andthe application of two addition cuts (see text) to xKa-lman.

10 2

0 0.5 1 1.5 2 2.5

|η|

Ru

xKalmaniPatRec + smearing

xKalman (no secondaries)iPatRec + smearing (no secondaries)



drop in efficiency from 86% to 77%, since the χ2 in xKalman is not as well tuned as in iPatRec.Cut (b) improves the rejection but by a smaller amount in both programs. There is no change inefficiency, but the fraction of secondaries is reduced from 1.8% to 1.6%. Cut (c) has been triedsuccessfully for xKalman: the fraction of secondaries is reduced to 1.5%, for a 2% fall in efficien-cy.

The effects of these various individual improvements are summarised in Table 6-21 andFigures 6-54 and 6-55 show the effect of cuts (a) and (c).

B-tagging in 3-DUnlike LEP vertex detectors, in ATLAS, the transverse and longitudinal impact parameter1 res-olutions, σ(d0) and σ(z0) sinθ, are quite different (see Section 4.4). Particle level studies havesuggested that as a consequence, the benefit to b-tagging provided by adding longitudinal in-formation may not be very great. Some preliminary studies confirmed that the gains were not

1. The relevant quantities are the impact parameters measured perpendicular to the jet axis.

Table 6-21 Rejections of u-jets after various improvements.


xKalman iPatRec

Default 50 ± 3 66 ± 3

Tag conversions 66 ± 5

χ2 cut 57 ± 4 78 ± 3

z cut 54 ± 4 73 ± 3

Hit quality cuts 70 ± 5

Figure 6-54 u-jet rejection as a function of |η| beforeand after a χ2 cut (iPatRec).

Figure 6-55 u-jet rejection as a function of |η| beforeand after hit quality cuts (xKalman).

20

30

40

5060708090

100

200

0 0.5 1 1.5 2 2.5

|η|

Ru

iPatRec (default)

iPatRec (with χ2 cut) 20

30

40

5060708090

100

200

0 0.5 1 1.5 2 2.5

|η|

Ru

xKalman (default)

xKalman (hit quality cuts)



great, although there is a belief that careful use of the longitudinal impact parameter may re-move some secondaries and poorly measured tracks. This is a topic for future study.

6.7.5 Degraded Performance

In this section, various sources of degradation are considered. A summary of the consequencesis given in Table 6-22. The effect of pile-up at the design luminosity has not been studied. How-ever, in the light of the results shown in Sections 3.5.5 and 3.6.5, the anticipation is that most ofthe potential pattern recognition problems are a direct result of the density of hits in a jet andwould not be enhanced significantly by pile-up. The effect of increased noise and decreased de-tector efficiency also need to be studied.

No B-layerThis study was performed using iPatRec,with and without the B-layer1. With the B-lay-er, the analysis was the same as before, name-ly: ≥ 9 precision hits, ≥ 2 pixel hits, a B-layerhit and |d0| < 1 mm. Without the B-layer, thecuts were changed to ≥ 8 precision hits, ≥ 1pixel hit and |d0| < 1 mm. The impact param-eter resolution without the B-layer forpT > 10 GeV is 35 μm instead of 23 μm and thedifference becomes more pronounced atlow pT. The rejections for u-jets (gluon jets) fallfrom 66 ± 3 (29 ± 1) to 28 ± 1 (24 ± 1).Figure 6-56 shows the u-jet rejection as func-tion of |η| with and without the B-layer.

Impact Parameter ResolutionIn order to estimate the effect of a degradedimpact parameter resolution, the impact pa-rameter was smeared by 15 μm. The averagedegradation of σ(d0) was ~4 μm, although thedegradation was greater for the tracks with larger pT, which are the tracks which make the mostimportant contributions to the b-tagging. The effect of this smearing is comparable with the dif-ference in resolution between xKalman and iPatRec. It also gives a feel for the effect of a √2increase in the spread of the beam spot. By design, the effects of misalignment should be evensmaller2 (see Chapter 9).

Event Weights

The likelihood ratio method requires the determination of a weight function. This function hasbeen determined using the Monte Carlo information, and the success of the method will be de-termined by how well this describes real data from ATLAS. To estimate the effect of these uncer-tainties, the weights of xKalman and iPatRec have been exchanged, resulting in only smallvariations of the rejection.

1. Rather than remove the B-layer, the efficiency was set to zero. This is conservative, since the inactiveB-layer contributes to multiple scattering and the creation of secondaries.

2. The target is for the effect of misalignments to increase the parameter errors by no more than 20%.

Figure 6-56 u-jet rejection as a function of |η| show-ing the effect of removing the B-layer.

10

10 2

0 0.5 1 1.5 2 2.5

|η|

Ru

iPatRec (default)

iPatRec (no B-layer)



6.7.6 Results for mH = 100 GeV

The analysis has been repeated in exactly the same way for mH = 100 GeV. For this mass, the jetsare softer (average jet pT = 60 GeV) and more uniform in η. The average jet multiplicity is6 charged tracks, 60% of which come from b-hadron decays. The average track pT above 1 GeVis 6.2 GeV. Since the pT spectrum is softer, the impact parameter resolution is degraded more bymultiple scattering. This is compensated by a reduced fraction of prompt tracks in the jet com-ing from fragmentation, which increases the relative significance of the daughters of theb-hadron decay. The rejections for εb = 50% are shown in Table 6-23.

The results for gluon jet rejections are lower than was reported in [6-13] due to the increasednumber of secondaries arising from the more realistic estimate of the material contained in theInner Detector. In the case of u-jets, the composition of the background is: 30% (40%) secondar-ies, 45% (50%) decays and 25% (10%) tracks from the primary vertex, reconstructed by xKa-lman (iPatRec). Unlike the events with mH = 400 GeV, for mH = 100 GeV, the background isdominated by hadron decays. In the case of gluons, the rejection is again limited by the gluonsplitting to heavy quarks (4% charm and 2% bottom), but to a lesser extent than formH = 400 GeV. Figures 6-57 and 6-58 show the mH dependence of the u-jet rejection as a func-tion of |η|.

6.7.7 Jet pT Dependence

The dependence on the jet pT has been studied for mH = 100 and 400 GeV and is shown inFigure 6-59. Both xKalman and iPatRec show the same trends: a sharp fall in the rejection atlow pT as pT tends to 0, and a slow degradation at high pT as pT increases.

Table 6-22 Rejections of u-jets as a result of degraded performance.


xKalman iPatRec

Default 50 ± 3 66 ± 3

No B-layer 29 ± 1

Degraded σ(d0) 47 ± 3 60 ± 3

Systematics in weights 47 ± 3 65 ± 3

Table 6-23 Rejections of various types of background jets for mH = 100 GeV.

Background jet Ru for εb = 50%

xKalman iPatRec

u-jet 80 ± 6 94 ± 5

gluon jet 41 ± 4 50 ± 2

c-jet 7.5 ± 0.3 8.0 ± 0.1



The sharp fall at low pT is due to:

• The decrease of jet multiplicity. For jet pT < 30 GeV, the jet multiplicity after selection cutsis 2.3 (to be compared with average of 4.3 for pT < 100 GeV) and 30% of the b-jets haveless than 2 tracks (compared with 10% for pT < 100 GeV).

• The worse impact parameter resolution arising from increased multiple scattering oftracks coming from a softer pT spectrum.

The individual contributions of these two effects can be estimated from Figure 6-60. In this fig-ure, the u-jet rejection from xKalman, plotted as function of the jet pT, is compared with the re-

Figure 6-57 u-jet rejection as a function of |η|, show-ing a comparison of different mH (xKalman).

Figure 6-58 u-jet rejection as a function of |η|, show-ing a comparison of different mH (iPatRec).

Figure 6-59 u-jet rejection as a function of jet pT. Figure 6-60 u-jet rejection as a function of jet pT,showing the effect of real compared to ideal impactparameter measurements (xKalman).

10 2

0 0.5 1 1.5 2 2.5

|η|

Ru

xKalman (MH=400 GeV)xKalman (MH=100 GeV)

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iPatRec (MH=400 GeV)iPatRec (MH=100 GeV)

10

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xKalman (MH=400 GeV)iPatRec (MH=400 GeV)

xKalman (MH=100 GeV)iPatRec (MH=100 GeV) 10

10 2

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Jet pT (GeV)

Ru

xKalmanGaussian resolution



jection expected from ‘Gaussian resolution’. The latter is obtained by using the impactparameter of the KINE track matching the reconstructed track, after smearing it by a Gaussiandistribution with a width of 20 μm (corresponding to the resolution seen for pT > 20 GeV - seeFigure 6-44). The difference between the two curves is the effect of multiple scattering andnon-Gaussian tails in the impact parameter distribution.

The slow degradation at high pT is the consequence of several factors:

• The increase in jet multiplicity due to the increase of the fragmentation component of thejet. Consequently, the discrimination between b- and u-jets is reduced. For jets withpT < 100 GeV, the number of tracks (after selection cuts) is 4.3 on the average, whereas it is10.4 for pT > 270 GeV.

• The increase in the fraction of secondaries contained in the jet: 1.3% for jet pT < 100 GeVand 2.2% for pT > 270 GeV.

• The difficulties of pattern recognition in more dense environment at larger jet pT valuesresult in more tails in the impact parameter distributions. The number of prompt trackswith |d0| > 3σ(d0) is 1.1% for pT < 100 GeV, and 2.3% for pT > 270 GeV. The correspond-ing values for secondaries are 52% and 61%.

The effect of reconstruction problems (essentially non-Gaussian tails in the impact parameterdistribution) can be estimated from the difference of the two curves in Figure 6-60.

The current analyses have used fixed cuts on track pT and cone size ΔR. Clearly the results dis-played in Figures 6-59 and 6-60 are very dependent on these cuts, and therefore the cuts will bestudied in further work to optimise the performance.

6.7.8 Impact on Physics

In this last section on b-tagging, the impact on the search for a possible signal from de-cays for 80 < mH < 120 GeV is evaluated using the analysis procedures and selection cuts fromprevious studies [6-14]. The much more detailed understanding of the b-tagging performanceachieved through the studies described above has permitted the implementation of a realisticparametrisation of the b-tagging performance into the fast simulation, ATLFAST [6-7]. This hasbeen used to study the signal from WH associated production followed by and W → lνalong with the associated backgrounds.

Efficiency-rejection curves have been taken from studies of mH = 100 GeV, corresponding toSection 6.7.6. xKalman with cut (c) of Section 6.7.4 has been used - iPatRec is expected to givevery similar results. The numbers used have been adapted to account for the different schemesof labelling jet flavour in the full-simulation studies and in the fast simulation program1; thisleads to a small correction factor to the b-tagging efficiencies2 quoted in the previous sections.The b-tagging performance has been parametrised in a consistent way and is shown inTable 6-24 for jets from u, d, s and gluons (not containing c-quarks or b-quarks in the final par-ton shower process) and in Table 6-25 for jets from charm. The rejections averaged over η

1. The fast simulation program has to handle many background sources with varying jet multiplicities andflavours.

2. This correction factor causes the b-tagging efficiencies to be modified from the starting values of 30, 40,50 and 60%.

H bb→

H bb→



and pT are shown in the second column as a function of the b-tagging efficiency. The other col-umns show the factors which are required to obtain the pT dependence discussed inSection 6.7.7.

The WH signal and all the background processes have been simulated and reconstructedthrough the fast simulation, modified to account for the b-tagging performance in a statisticalway for each reconstructed jet (including the pT dependence described in Tables 6-24 and 6-25).The results are shown in Table 6-26 for an integrated luminosity of 3 × 104 pb-1 and formH = 100 GeV. The background processes can be separated into irreducible background con-taining real b-jets and reducible background (predominantly from W+jet events) containingnon-b jets wrongly tagged as b-jets. The table includes the ratio of reducible to irreducible back-ground, Rred/irred, along with the signal-to-background ratio, S/B, and the significance ex-pressed crudely as S/√B. It can be seen that the ratio Rred/irred increases from a safe value of 0.26for a b-tagging efficiency of 33% to a very large value of 4.12 for a b-tagging efficiency of 63%.At the same time, the signal-to-background ratio decreases by about a factor of 6 from 3.6% to0.6%. The optimal result, corresponding to a significance of 2.43, is obtained for a b-tagging effi-ciency of 53%, for which the reducible background from non-b jets appears to be at the samelevel as the irreducible one - a potentially dangerous situation since the reducible backgroundsusually suffer from the largest systematic uncertainties.

Clearly this channel remains a difficult challenge at the LHC and needs to be studied at high lu-minosity. The uncertainties on the b-tagging performance discussed above in terms of possibleimprovements or degradations do not change the results shown in Table 6-26 by more than 10%for b-tagging efficiencies below 50%, since the dominant background in these cases is the irre-ducible background.

Table 6-24 Rejections from vertex tagging for jets, not containing any heavy flavour components, from Higgsdecays with mH = 100 GeV as a function of b-tagging efficiency. The pT dependence is given in the last five col-umns.

εb (%) Rj(ave) Rj(pT)/Rj(ave)

15 < pT < 30 30 < pT < 45 45 < pT < 60 60 < pT < 100 100 < pT

33 1400 ± 400 0.11 0.35 1.80 1.80 1.80

43 220 ± 30 0.28 0.49 2.16 2.16 1.58

53 91 ± 7 0.24 0.51 1.75 2.10 1.95

64 32 ± 2 0.18 0.59 1.50 2.11 1.94

Table 6-25 Rejections for c-quark jets from Higgs decays with mH = 100 GeV as a function of b-tagging effi-ciency. The pT dependence is given in the last five columns.

εb (%) Rc(ave) Rc(pT)/Rc(ave)

15 < pT < 30 30 < pT < 45 45 < pT < 60 60 < pT < 100 100 < pT

33 22.9 ± 2.0 0.44 0.68 1.10 1.57 2.17

43 10.8 ± 0.6 0.58 0.66 1.23 1.59 1.13

53 6.7 ± 0.3 0.58 0.75 1.40 1.54 1.40

64 4.2 ± 0.1 0.60 0.82 1.22 1.29 1.28



Finally, it is important to note that b-jets can be tagged also by soft leptons:

• Using the TR information and the EM calorimeter for electrons with pT > 1 GeV(see Section 6.2.2),

• Using the hadron calorimeters and the muon system for muons with pT > 2 GeV.

These have the potential of substantially improving the sensitivity to a possible signal in thischannel, provided that the rejection of non-b jets achieved with these methods is significantlybetter than that achieved with vertexing. This optimistic assumption, combined with the antici-pation of an efficiency for tagging b-jets around 50% (along the lines of Section 6.2.2), has beenused to obtain the numbers1 shown in the last column of Table 6-26.

1. The addition input used is that the inclusive branching ratios for b → eX and μX are both ~20% (mayinclude decays of charm mesons) and allowance is made for double tags: εtot = εvtx+εlept-εvtxεlept.

Table 6-26 Expected numbers of events for signal from Standard Model WH (mH = 100 GeV) associated pro-duction followed by and various backgrounds, corresponding to an integrated luminosity of3 × 104 pb-1. Numbers are shown for different tagging efficiencies. The last column includes a soft lepton tag(see text).

Expected numbers of events

Tag Vertex Vertex + lepton

εb (%) 33 43 53 64 62.4

εj (%) 0.07 0.46 1.1 3.1 1.1

εc (%) 4.3 9.2 14.9 23.8 14.9

Signal S

WH, 130 210 330 485 450

Irreducible bgnd

WZ, 180 300 440 640 590

W 1140 1850 2900 4090 3950

1100 1870 3000 4600 4000

230 370 580 820 800

Reducible bgnd

W 360 1100 2100 4400 2350

W 270 1300 2400 9800 2400

Wbj 60 310 1100 9000 1300

Wcj 170 1000 4300 32000 4300

Wjj 100 300 1580 21000 1580

Rred/irred 0.26 0.65 1.16 4.12 0.91

Total bgnd B 3610 8400 18400 86350 21270

S/B 3.6% 2.5% 1.8% 0.6% 2.1%

S/√B 2.16 2.29 2.43 1.65 3.09

H bb→

H bb→

Z bb→

bb

tt WWbb→

tb Wbb→

bc

cc



6.7.9 Conclusions on b-Tagging

The work described above and in Section 5.2 has led to a considerably improved understandingof the Inner Detector performance related to heavy-flavour tagging using vertexing in high-pTjets:

• Two quite different reconstruction algorithms (iPatRec and xKalman) have been testedon the complex problem of b-tagging using vertex information. The results found are inreasonable agreement, indicating that they reflect the actual performance of the detectorwhich was simulated. The differences between the two approaches are believed to be un-derstood in terms of different pixel-clustering in the B-layer (leading to different impactparameter resolutions) and different internal cuts in the algorithms themselves. Thisdemonstrates the need for some harmonisation of future work in this field.

• For low-pT jets (for example, as produced by Higgs decays with mH = 100 GeV), the u-jetrejection Ru is limited by physics (decays) whereas for high-pT jets (mH = 400 GeV), therejection is limited by tracks from secondary interactions and to some extent by the jetmultiplicity itself (at the highest pT studied here). This demonstrates the need to rejecteven more of the secondaries (mainly conversions) and work is in progress in this direc-tion along the lines of the results presented in Section 6.3.2. The rejection of gluon jets Rgis limited by the heavy quark content of the jets; while the rejection of c-jets Rc is limitedby the lifetime of c-hadrons.

• A significant dependence of Ru on the jet pT has been found and is believed to arise fromphysics reasons and the cuts (in particular the cone size) used in the current analysis,rather than the intrinsic detector performance. This needs further study to see if it can beimproved and consequences on physics remain to be investigated.

• The b-tagging results presented above have been applied to the particular case ofdecays. The results are encouraging but show the necessity to further improve the per-formance. Since the results depend on the pT dependence of the rejection, there is the pos-sibility of optimisation with improved cuts. The basic results presented in this section arereasonably conservative, but improved b-tagging algorithms are under study, e.g. usingthe z-information. The first results indicate that there is some room for improved per-formance and therefore of greater sensitivity to the various physics signals involvingb-jets. Combination with lepton should also be studied in detail.

H bb→



6.8 References

6-1 ATLAS Collaboration, Letter of Intent, CERN/LHCC/92-4.


6-3 A. Clark et al., ATLAS Internal Note, INDET-NO-015.

6-4 D. Froidevaux et al., ATLAS Internal Note, INDET-NO-017.

6-5 T. Pal et al., ATLAS Internal Note, INDET-NO-127.

6-6 D. Froidevaux et al., ATLAS Internal Note, DAQ-TR-201.

6-7 E. Richter-Was et al., ATLAS Internal Note, PHYS-NO-079.

6-8 S. Schuh et al., ATLAS Internal Note, PHYS-NO-070.


6-10 ATLAS Collaboration, Technical Proposal, CERN/LHCC 94-43.


6-12 ALEPH Collaboration, Phys. Lett. B313 (1993) p535.

6-13 I. Gavrilenko et al, ATLAS Internal Note, INDET-NO-115.

6-14 D. Froidevaux and E. Richter-Was, Z. Phys. C67 (1995) 213.


7 Level-2 Trigger 195

7 Level-2 Trigger

7.1 Introduction

The Level-1 trigger system makes use of information from a subset of detectors, the calorimeterand muon systems, at a reduced granularity. The role of the Level-2 trigger is to utilise full gran-ularity information from the majority of detectors, but in most cases in limited regions identi-fied by Level-1. This includes information from the Inner Detector. A search for tracks in theTRT and precision layers can be used to complement the information from the calorimeter andmuon systems. This, together with a refinement of the information from the detectors used atLevel-1, allows a reduction of ~100 in the rate at which events are passed on to the Event Filter.

It should be noted that the scope of the discussion here is limited to demonstrating that the pro-posed detector design is capable of providing the required trigger performance. The expectedperformance is illustrated with a few key examples. Some of the results presented are based onoffline code; others are the results of algorithms compatible with candidate trigger implementa-tion schemes. The issues of trigger performance will be addressed much more fully in a triggerdocument to be submitted at a later stage. In particular, the implementation issues are still un-der consideration. It should be noted that the overall optimisation of the trigger implementa-tion, taking into account the required processing power, data bandwidth, and cost may lead to aloss of performance compared to that presented here.

7.2 Level-2 Requirements for the Inner Detector

The trigger strategies utilised within the Inner Detector fall into two categories:

High-pT TriggerA search for a high-pT track, pT > ~5 GeV, in a part of the detector (Region of Interest or ROI)identified by the Level-1 system. This class of trigger is designed to accept channels containinghigh-pT electrons or muons in the final state, either from known physics sources (W, Z, top) orfrom new physics (Higgs, supersymmetry, new gauge bosons etc.).

Low-pT TriggerAn un-guided search in the TRT for tracks with pT > ~0.5 GeV, extrapolated into the precisionlayers when necessary. This trigger is designed for B-physics channels which will be acceptedon the basis of topologies of low-pT tracks.

It is important to be able to tune the trigger selections as the LHC luminosity increases. It is fore-seen that the relative importance of different physics channels will change with time, moreweight being given to the low-pT channels in the initial lower luminosity running.

The selected data will be processed by feature extraction (FEX) algorithms to extract quantitieswhich are used in the global trigger decision. The methods used will, in general, be simpler andless iterative than in offline code. The algorithms should not be too dependent on the ultimateresolution of the detector since the full set of calibration data (alignment offsets, drift-time cali-bration constants, etc.) may not be available at the trigger level.


196 7 Level-2 Trigger

For the high-pT triggers, the principal requirements arise from the need to reduce the rate ofLevel-1 high-ET triggers from isolated EM clusters by rejecting background from minimum biasand jet events. This leads to the following two requirements:

• Efficiency for finding an isolated high-pT electron track of better than 90%, excluding theloss of tracks with very hard or multiple bremsstrahlung which would not be recoveredoffline.

• Reduction of the Level-2 accept rate by a factor of ~10 with respect to the rate of eventspassing the Level-2 calorimeter selection, at the design luminosity of 1034 cm-2s-1.

For B-physics, the goal is to maintain good efficiency for selected channels whilst keeping theLevel-2 accept rate for these events below a maximum value of ~800 Hz. The precise require-ments vary according to the channel to be selected; a few examples are given in Section 7.4 be-low.

7.3 Performance of High-pT Triggers

Within the trigger schemes currently under consideration, the Level-1 accept rate is dominatedby the triggers from single isolated electromagnetic (EM) clusters. It is envisioned to use an EMcalorimeter ET threshold of ~20 GeV for low luminosity running and ~30 GeV at the design lu-minosity. At Level-2, the calorimeter trigger selections reduce the rate by a factor ~10 (for an ETthreshold of 30 GeV) compared to Level-1 whilst maintaining a high efficiency for isolated elec-trons and photons. The requirement for the Inner Detector at Level-2 is to provide track infor-mation for the ROI. Requiring the presence of a high-pT track and matching its parameters tothe Level-2 calorimeter measurements enables a further reduction of the trigger rate, whilstmaintaining good efficiency.

The trigger performance of the Inner Detector has been determined using samples of single par-ticles with and without pile-up for efficiency and fake rate measurements and di-jet events withand without pile-up to determine trigger rates. The latter was produced from 5 × 105 generatedPYTHIA di-jet events. All samples were passed through a full GEANT simulation of the Inner De-tector and calorimeter. A loose set of calorimeter cuts, designed to reject events that wouldclearly fail the Level-2 trigger, were then applied to the di-jet sample. Pile-up was added to theresulting sample of ~2300 events. The detector simulation includes the effects of inefficiencyand noise in the SCT and pixel layers. The effects of mis-alignment have not been included inthe present study.

The analysis was performed within the framework of the ATLAS trigger simulation package(ATRIG). This provides information on ROIs identified by a simulation of the Level-1 trigger.The Level-2 track searches are performed within these regions. In the current trigger implemen-tation models, these searches are performed separately in the TRT and precision layers. Thetrack and calorimeter information is combined in order to form a global Level-2 trigger deci-sion. The complementarity of the TRT and precision detector information can be utilised so as tomaintain a high efficiency for isolated electrons whilst giving the required reduction in the trig-ger rate.

For both the precision detector and the TRT, a histogramming method is used to select sets ofpoints to be passed on to a fit. The advantage of such a method is that execution time scalesmore slowly with occupancy than a combinatorial method (typically as N logN for the TRT al-gorithm). By fitting only to the points in selected bins of the histogram, the number of hit com-



binations and therefore the time required for the fit is significantly reduced. The track search isperformed in the R-φ plane for the barrel and the φ-z plane for the end-cap region. To a good ap-proximation (within the pT range of the search) tracks from the primary vertex are straight inthese coordinate systems. A histogram is constructed of the number of hits in straight roads inthe appropriate plane. The roads are described by the intercept and slope of their centre line. A2-D histogram is formed as a function of these quantities. The maximum absolute value of theslope considered defines the minimum pT of the search. If the number of hits in a bin is abovesome threshold, the points are used in the subsequent fit.

7.3.1 Feature Extraction in the Precision Tracker

For the precision layers (SCT and pixels), the data input to the histogramming stage are 3-D re-constructed points (space-points). In the first stage of the algorithm, clusters are formed fromhits on adjacent strips or pixels. In the case of the SCT, information from the stereo and φ-stripsis combined to form space-points. The maximum absolute value of the slope used for the histo-gram corresponds to a minimum pT of 5 GeV. The results shown here are based on a histogramsize of 100 × 100 bins. At least 4 points are required in a histogram bin to carry on to a fit. A leastsquares straight-line fit is performed independently in the R-φ and φ-z planes with all combina-tions of four or more points, using at most one per detector plane. The information for the high-est-pT track candidate, with pT > 5 GeV, is passed on to be used in the global Level-2 decision.No other track quality cuts are applied at the fitting stage. The selection of points used in the fitis determined entirely by the histogramming process. This algorithm is described in more detailin [7-1].

The bin size, chosen for illustration here, corresponds to a fairly fine binning. The optimum his-togram bin size depends on the choice of technology for the trigger implementation and is a bal-ance between the times spent on filling the histogram and performing the fit. With the simple fitused here, a small loss of efficiency is seen with coarser binning. An alternative algorithm basedpurely on a fit and using only φ-information from the SCT has previously been studied [7-2].

Figure 7-1 Efficiency to find a track in the precisiondetector for single muons and electrons.

Figure 7-2 Efficiency to find tracks in the precisiondetector for single electron with pile-up at 1034 cm-2s-1

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The efficiency for finding a track in the precision detector is shown for single particles as a func-tion of |η| in Figure 7-1. There is a loss of electron tracks due to interactions and bremsstrahl-ung; this is more pronounced in the end-cap region where the tracks traverse more material.With the addition of pile-up at the design luminosity of 1034 cm-2s-1, there is a small decrease inthe efficiency for finding a track. The effect of pile-up on track measurements can be illustratedby requiring a match of the measured φ of the track to the true initial trajectory of the electron.As can be seen in Figure 7-2, a small proportion of tracks (~2%) are not well matched. This isdue to fakes and tracks ‘spoilt’ by the loss of the correct hits and the inclusion of hits frompile-up. However, it should be noted that in some cases it is possible for an event with an isolat-ed high-pT track to produce a match to the calorimeter, and hence correctly trigger, even thoughthe track parameters do not correspond well to the initial trajectory of the triggering electron. Atrue determination of efficiency results from considering the overall global Level-2 decision,which is discussed in Section 7.3.3.

In order to determine the probability of find-ing a fake or background track, searches weremade within regions (Δη × Δφ = 0.2 × 0.2, cor-responding to the typical size of a ROI) ofpile-up events at the design luminosity of1034 cm-2s-1. The resulting probability of find-ing a track is shown as a function of |η| inFigure 7-3 for tracks with reconstructedpT ≥ 7 GeV and for two different values of thecut on the minimum number of space-pointsrequired on the track. When at least 4space-points are required, a fake track is foundin about 2% of cases, on average. This is atleast an order of magnitude larger than therate of real tracks with pT > 7 GeV in pile-upevents. However, it should be noted that onlya small fraction of these tracks will match witha cluster in the calorimeter and hence give atrigger. This will be discussed further inSection 7.3.3. If the minimum number ofspace-points required is increased to 5, theprobability of finding a track falls to an average of 0.27%. There is a corresponding loss in effi-ciency for single electrons with pile-up of ~2%.

7.3.2 Feature Extraction in the TRT

In the case of the TRT, the input to the algorithm is the positional information for all straws inthe ROI. The result is based on the number of straws along the trajectory of a track candidatewith and without hits (signals passing a low threshold), the number of straws with a drift-timemeasurement (drift-time hit), and the number of straws with a signal passing a higher threshold(TR hit).

The histogramming stage is based on a Hough transform. Each straw is considered as twoboundaries in φ. The histogramming process proceeds in steps defined by the positions of theseboundaries: typically ~3000 steps are used when scanning across an ROI of width Δφ = 0.2.

Figure 7-3 The probability of finding a track(pT ≥ 7 GeV) in the precision detector in aΔη × Δφ = 0.2 × 0.2 region of a pile-up event as a func-tion of |η|.

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Once the track candidates have been found a subsequent ‘fine tuning’ stage makes a parabolicfit to the measured points. The drift-time information is included at this stage [7-3][7-4]. In theend-cap region, an η measurement (and therefore a direct pT measurement) is derived from thepositions in z of the first and last straws with hits along the candidate track direction combinedwith the knowledge of the inner and outer end-cap wheel radii (this only works for |η| < 2.2).

The track search may result in several candidate tracks with pT above the chosen threshold. Ofthese, the best candidate is chosen on the basis of a maximum-likelihood parameter L, which isdefined for each candidate track as:

where:

• N1 is the number of straws with hits.

• N2 is the number of straws without a hit.

• N3 is the number of drift-time hits.

• N4 is the number of high-threshold TR hits.

The weights w1 (positive) and w2 (negative) are determined from the probability for a high-pTtrack to produce a hit (~0.95) and the probability of a hit from background. The highest qualitytrack candidate is expected to maximise the difference N1−N2. Similarly, w3 is determined fromthe expected fraction of drift-time hits. This fraction decreases from ~93% at low luminosity to~70% at high luminosity due to shadowing effects (see Figures 3-80 and 3-81) and also variesbetween the most and least occupied layers. The value of w4 is determined from the expectedfraction (~0.25) of TR hits. These weights were determined in three |η| regions, one for the bar-rel, and two for the end-cap. Of the track candidates found in each ROI with L above an(|η| dependent) cut, the track with the highest pT is chosen, and its parameters are passed onto be used in the global Level-2 trigger decision.

Figure 7-4 TRT quality parameter L for electrons(open) and fake or background (filled) tracks.

Figure 7-5 TRT quality parameter L for electrons(open) and fake or background (filled) tracks.

L wiNii 1=

4

∑=

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0.02

0.03

0 50 100 150 200

L

1/N

dN

/dL

0

0.005

0.01

0.015

0.02

0.025

0 50 100 150 200 250

L

1/N

dN

/dL



The distribution of L is shown for events with pile-up in Figures 7-4 and 7-5 for two regions,1.1 < |η| < 1.5 and 2.0 < |η| < 2.5 respectively. The open histograms were obtained for ROIscontaining a high-pT electron and pile-up, whereas the filled histograms were obtained for re-gions of the same size containing only pile-up hits. As expected, the large number of measure-ments in the TRT provides excellent separation between signal and background. The tails seenat low values of L for the electrons are due mostly to bremsstrahlung effects. Thus a significantfraction of the electrons rejected by the cut on L would in any case fail the offline analysis selec-tions.

The measured values for efficiency and background, after a cut on L, are shown in Table 7-1.Background efficiency is defined as the fraction of ROIs in pile-up events at the design luminos-ity that contain a track. The background track candidates were divided into those from regionscontaining a real high-pT track from pile-up (occurring at a typical rate of ~2 × 10−3 per ROI forpT > 5 GeV) and those where the track candidate was a fake. Results are shown for different

Table 7-1 Efficiency and background rates for pT = 20 GeV and 40 GeV electrons with pile-up for a cut of5 GeV on the pT of the reconstructed track. Where no tracks were found, 95% CL upper limits are given.

|η| Test Electron efficiency (%) Background efficiency (%)

pT = 20 pT = 40 Fake Real Total

Hits 86 92 <0.06 0.55 ± 0.13 0.55 ± 0.13

0 - 0.65 Hits+TR hits 86 92 <0.06 0.51 ± 0.10 0.51 ± 0.10

Hits+d-t 86 91 <0.06 0.50 ± 0.09 0.50 ± 0.09

Hits+TR+d-t 85 92 <0.06 0.45 ± 0.09 0.45 ± 0.09

Hits 85 88 0.77 ± 0.15 0.5 ± 0.1 1.3 ± 0.2

0.65 - 1.1 Hits+TR hits 84 87 0.59 ± 0.13 0.38 ± 0.11 0.97 ± 0.17

Hits+d-t 85 88 0.05 ± 0.04 0.23 ± 0.08 0.28 ± 0.08

Hits+TR+d-t 85 87 <0.07 0.20 ± 0.07 0.20 ± 0.07

Hits 85 92 0.26 ± 0.09 0.06 ± 0.04 0.32 ± 0.10

1.1 - 1.55 Hits+TR hits 85 92 0.17 ± 0.07 0.03 ± 0.03 0.21 ± 0.08

Hits+d-t 86 92 0.11 ± 0.05 0.08 ± 0.04 0.18 ± 0.07

Hits+TR+d-t 86 93 0.08 ± 0.04 0.08 ± 0.04 0.15 ± 0.06

Hits 85 95 0.63 ± 0.13 0.09 ± 0.06 0.74 ± 0.15

1.55 - 2.0 Hits+TR hits 85 96 0.29 ± 0.09 0.09 ± 0.06 0.38 ± 0.11

Hits+d-t 84 94 0.18 ± 0.07 0.10 ± 0.05 0.28 ± 0.08

Hits+TR+d-t 84 96 0.16 ± 0.07 0.10 ± 0.05 0.25 ± 0.08

Hits 85 91 2.50 ± 0.25 0.5 ± 0.1 3.0 ± 0.3

2.0 - 2.5 Hits+TR hits 85 91 1.6 ± 0.2 0.5 ± 0.1 2.1 ± 0.2

Hits+d-t 85 91 0.88 ± 0.14 0.36 ± 0.09 1.2 ± 0.2

Hits+TR+d-t 85 95 0.75 ± 0.13 0.29 ± 0.08 1.04 ± 0.15



|η| regions and for four constructions of L which make use of different combinations of theavailable information:

1. Only the number of straws with and without hits.

2. Include additionally TR hits.

3. As for 1., but including drift-time (d-t) hits (this would be used for high-pT muons).

4. Include all information.

Due to the geometry of the TRT, the actual size of the area in Δη × Δφ space scanned by the algo-rithm varies from 0.6 × 0.2 in the barrel to 0.2 × 0.2 over most of the end-cap region and to0.5 × 0.2 for the last |η| bin shown in the table. The largest fake rates (~0.9% when using hitsand drift-time) are observed in the last bin. If all information is used, including TR (i.e. for anelectron trigger), the fake rates are below 0.1% over much of the |η| range, increasing to 0.75%in the highest |η| bin.

The cuts on L were chosen so as to obtain an approximately constant electron efficiencyover|η|. The value for the efficiency depends on the pT of the track, varying from ~85% atpT = 20 GeV to ~93% for pT = 40 GeV tracks, see Figure 7-6. Most of the losses are due to hardbremsstrahlung and should not really be considered as trigger inefficiency.

Finally, Figure 7-7 shows, as a function of |η|, the probability of finding a track passing the se-lection cuts (pT > 5 GeV plus a cut on L) in a region of equivalent size to an ROI for pile-upevents. Results are shown for the case when the information from hits and drift-time is used.The background rate can be seen to be dominated by real high-pT tracks in pile-up events overmuch of the |η| range. (The real track rate is plotted as a single average value for the range0.65 < |η| < 2.0).

Figure 7-6 Efficiency as a function of |η| for singleelectrons with pile-up when hit and drift-time informa-tion is used.

Figure 7-7 Fraction of background events with areconstructed track, ‘fake’ or ‘real’, with pT > 5 GeV asa function of |η| using hits and drift-time information.

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Real Background Tracks



7.3.3 Global Performance

In order to reduce the rate of triggers from jets, whilst maintaining a good efficiency for isolatedhigh-pT electrons, the track parameters determined by the Inner Detector are combined with thecalorimetry information. This is an area of continuing study. The intention here is to show thatthe required performance can be achieved using a given combination of selection cuts. The re-sults of a more detailed optimisation of the selection will be reported at a later stage.

The measurements of global Level-2 trigger performance were made on samples of single elec-trons and jet events with and without pile-up. A Level-2 calorimeter selection was appliedbased on a) the transverse energy of the EM calorimeter in a 3×7 cell cluster in η × φ, b) thetransverse hadronic energy (in a region Δη × Δφ = 0.2 × 0.2) and c) the ratio of EM energy in awide 7×7 cell cluster to that in a narrower 3×7 cluster. The latter provides a measure of isolation.The following cuts were used:

a. ET ≥ 17 GeV (low luminosity) or ET ≥ 27 GeV (high luminosity)

b. ET(Hcal) ≤ 1.5 GeV

c. E3×7 / E7×7 ≥ 0.905

This selection does not make use of the complete set of calorimetry information which will beavailable at Level-2, but is sufficient to provide a reference point for subsequent efficiency andrate measurements incorporating the Inner Detector information. Efficiencies are quoted as afraction of the number of events passing this calorimeter selection. The trigger rates are deter-mined from knowledge of the number of events generated using an estimate of the cross-sec-tion for the events produced, and applying a correction for the bias introduced by the chosenkinematic cuts [7-5]. Using this normalisation, the trigger rate after the Level-2 calorimeter trig-ger is estimated to be 5 kHz at the design luminosity of 1034 cm-2s-1. There is an uncertainty ofthe order of a factor 2 in the value for the cross-section. If necessary a further factor of 2 reduc-tion in trigger rate could be obtained by raising the ET threshold by ~5 GeV.

An initial requirement for the Inner Detectortrigger is that a track be found with a pT abovesome threshold.The trigger efficiency is shownin Figure 7-8 as a function of pT cut for the pre-cision tracker and the TRT.

A cut of pT ≥7 GeV results in a trigger rate of3.5 kHz for the SCT and an efficiency for30 GeV electrons with pile-up of 96.7% (seeTable 7-2). The efficiency of the TRT triggerfalls more rapidly with the value of the pT cutdue to bremsstrahlung energy losses of elec-trons before they reach the TRT. A cut ofpT ≥ 5 GeV gives an efficiency of 92.4% forelectron events with pile-up and a trigger rateof 2.2 kHz.

The higher trigger rate for the precision detec-tor is due to a higher level of fakes arisingfrom the requirement for a minimum of only 4space-points on a track. These fake tracks can be rejected by requiring a match in azimuthal an-gle, φ, between the track and the calorimeter cluster as will be shown below. Alternatively, if the

Figure 7-8 Efficiency as a function of pT cut value forthe TRT and precision detector.

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30 GeV e- no pile-upprecision trackTRT track



cut on the number of precision space-points required on a track is increased to ≥ 5, the triggerrate is reduced to 1.7 kHz, with a 2% drop in efficiency for electrons with pile-up.

The distribution of the difference in azimuthal angle between the extrapolated track and the cal-orimeter cluster position (φTrk−φEcal) is shown for the precision tracker and TRT in Figures 7-9and 7-10 respectively. The distribution for electrons is very narrow compared to that for jetevents. Thus a cut on this quantity provides good discrimination. A rather loose cut was ap-plied (|φSi−φEcal|<0.03 and |φTRT−φEcal| < 0.05) so as to maintain good efficiency for electronswith pile-up. After these cuts, the trigger rates for the individual SCT and TRT triggers are both~1.6 kHz.

Table 7-2 Efficiencies for single pT = 30 GeV electrons with and without pile-up and corresponding trigger ratesfor jet events with pile-up after the high luminosity Level-2 calorimeter trigger and with additional track/EM clus-ter matching requirements: Si : | φSi−φEcal | < 0.03 and ET/pT < 4, TRT : | φSi−φEcal | < 0.05 and ET/pT < 5,‘ID’ requires the presence of a precision (Si) track and TRT track.

SelectionRequirements

Efficiency (%) Trigger rate (kHz)

Electron Electron + pile-up

L2CAL 100 100 5.0

Si 95.2 96.7 3.5

Track TRT 93.7 92.4 2.2

ID 90.5 89.6 1.6

Si 94.6 94.9 1.4

φ and ET/pT match TRT 93.2 91.4 1.5

ID 90.1 88.1 0.7

Figure 7-9 The difference in azimuthal angle betweenthe extrapolated precision track and EM cluster.

Figure 7-10 The difference in azimuthal anglebetween the extrapolated TRT track and EM cluster.

0

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The Level-2 trigger rate can be reduced to anacceptable level by demanding a match be-tween track and calorimeter cluster for boththe precision detector and TRT and by apply-ing an additional very loose cut on the ratio ofthe ET of the calorimeter cluster to the pT ofthe track (ET/pT < 4 for the precision trackerand ET/pT < 5 for the TRT). With these cutsthe trigger rate is reduced to 0.7 kHz with anefficiency for 30 GeV electrons with pile-up of88%. The efficiency is shown as a function of|η| in Figure 7-11.

At low luminosity, a trigger threshold of~20 GeV is envisioned to be used for isolatedhigh-pT tracks. The results for 20 GeV elec-trons and jet events, both without the additionof pile-up, are shown in Table 7-3. The efficien-cy for finding a track in the precision detectorand TRT is slightly lower at this energy than at30 GeV. After applying the same selection cutsas for the events with pile-up and requiring a match between the track and calorimeter clusterin both the precision detector and the TRT, a trigger rate of 0.3 kHz is obtained with an efficien-cy of 86.1% for the electron events. Should a higher Level-2 trigger rate be acceptable at low lu-minosity, an efficiency of 97% could be obtained at a increased trigger rate of 0.8 kHz byaccepting events with a valid track/EM cluster match for either the precision tracker or the TRT.

Table 7-3 Efficiencies for single electrons of pT = 20 GeV without pile-up and the corresponding trigger rate forjet events without pile-up after the low luminosity Level-2 calorimeter trigger and with additional track/Ecal clus-ter matching requirements: Si : | φSi−φEcal | < 0.03 and ET/pT < 4, TRT : | φSi−φEcal | < 0.05 and ET/pT < 5,‘ID’ requires the presence of a precision (Si) track and TRT track.

Selection Requirements Efficiency (%) Trigger rate (kHz)

L2CAL 100 2.5

Si 93.9 0.6

Track TRT 90.3 0.9

ID 86.6 0.5

Si 93.2 0.4

φ and ET/pT match TRT 90.1 0.7

ID 86.1 0.3

Figure 7-11 Level-2 trigger efficiency for single iso-lated electrons with pT = 30 GeV as a function of |η| at1034 cm-2s-1, including the φ and ET/pT matching.

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7.4 B-physics Triggers

For B-physics studies, the Level-1 trigger will be an inclusive muon trigger with a pT thresholdof 6 GeV. This will be refined at Level-2 using information from the precision muon chambersand the Inner Detector. The rate of the muon triggers at Level-2 is expected to be ~4 kHz at a lu-minosity of 1033 cm-2s-1. The role of the Inner Detector is to provide information on low-pTtracks which will enable the rate to be reduced further by demanding additional signatures forselected processes. These include channels important for CP-violation studies in the B-systemand for the measurement of oscillations

• → J/ψ with J/ψ → e+e− provides a precise measurement of sin2β, provided that alow-pT threshold of 0.5 - 1 GeV for electrons can be attained.

• and with and φ → K+K− provide excellent sensitiv-ity for the measurement of xs.

• → π+π− provides good sensitivity for the measurement of sin2α.

A key component of the trigger menu for B-physics channels will be an electron-pair triggerwhich will select processes with an inclusive J/ψ → e+e− decay, including the channel

→ J/ψ . This channel is representative of the requirements on the Inner Detector in termsof track finding efficiency and particle identification, and is used to illustrate the tracker per-formance. The Level-2 accept rate for this trigger is required to be < ~400 Hz. Some preliminaryresults are also shown for the two other channels mentioned above.

These and other channels will be addressed in more detail, including a consideration of imple-mentation issues, in a trigger document to be submitted at a later stage. Other methods whichare interesting for selecting B-physics channels make use of impact parameter measurements orcuts on reconstructed secondary vertices. Level-2 algorithms using these techniques are current-ly under study.

The performance results shown below were obtained using samples of simulated events fromthe channels listed above where the other b-quark in the event decayed semi-leptonically togive a muon (providing a Level-1 trigger and tag) and background events from the process

. These samples were generated using PYTHIA. The pairs were produced inparton showers following a hard QCD process. The events were passed through a full simula-tion of the detector using GEANT. The final state particles of the signal processes were requiredto have pT > 0.5 GeV and to be within the range |η| < 2.5. To simulate the effect of the Level-1and Level-2 muon triggers, the muon was required to have a pT > 6 GeV and |η| < 2.5.

For the trigger rate calculation, the full background sample was taken to represent the expected4 kHz Level-1 muon trigger rate. The proportion of events passing the trigger selection wasconverted to the corresponding rate. The efficiency measurements are designed to show theperformance of the trigger for events which would be used in offline analyses. Therefore signalevent samples were selected as sub-sets of the generated events by applying cuts to the recon-structed tracks or at the particle level. Details of these cuts are given in the relevant sub-sectionsbelow.

As there is no externally defined ROI in these events (other than that for the Level-1 triggermuon), the first step of the Inner Detector trigger is to perform a search for tracks in the wholevolume of the detector. Since the signatures for many processes involve low-pT tracks, good ef-ficiency must be maintained down to a pT of 0.5 GeV.

Bs0

Bd0

Ks0

Bs0

D→ s+−

π±Bs

0Ds

+− a1±→ Ds

+− φπ+−→

Bd0

Bd0

Ks0

pp bbX μX'→→ bb



The program xKalman (see Section 2.5.2.3) was used for these studies. It uses the same histo-gramming method as described in Section 7.3.2 above for the high-pT TRT trigger. It then ex-tends the search road into the precision detector to pick up hits from these layers. The hitinformation is used in a helix fit using Kalman filtering and smoothing techniques which takeinto account multiple scattering and energy loss via bremsstrahlung. Note that it is the informa-tion from the individual hits in the precision tracker that is used in the fit, rather than recon-structed space-points used in the algorithm described in Section 7.3.1.

7.4.1 B0d → J/ψ K0

s

The efficiency for reconstructing electrons from J/ψ decays is shown in Figures 7-12 and 7-13 asfunctions of pT and |η|. Whilst there is some loss of efficiency for very low-pT tracks, an aver-age reconstruction efficiency of 90% per electron is achieved (for pT > 0.5 and |η| < 2.5). It canbe seen that most of the loss of efficiency is in the end-cap region of the detector, where particlestraverse the most material. For comparison, the efficiency for reconstructing muons from thedecay J/ψ → μ+μ− is shown. It is close to 100% over the entire rapidity range.

Electron identification relies on the transition radiation (TR) capability of the TRT. The fractionR1 of TR hits on a track provides a means of discriminating between electron and hadron tracks.In order to identify an e+e− pair, a further quantity, R12, is defined which is the ratio of the sumof the numbers of TR hits for both tracks divided by the sum of the total numbers of TRT hits.These quantities can be used together to significantly reduce the contribution of fake pair com-binations which include at least one hadron. 2-D distributions of R1 and R12 are shown fortracks with pT > 0.5 GeV in Figures 7-14 and 7-15 for signal (e+e− from J/ψ decays) and back-ground pair combinations respectively. (A point is plotted for each track, thus each pair is en-tered twice in the histogram.)

Figure 7-12 Efficiency for reconstructing leptons fromJ/ψ decays as a function of pT. The electron pT spec-trum is also shown (arbitrary scale).

Figure 7-13 Efficiency for reconstructing leptons fromJ/ψ decays as a function of |η|. The electron |η| spec-trum is also shown (arbitrary scale).

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The trigger efficiency measurements were made using a signal sample of J/ψ → e+e− events af-ter a cut pT > 1 GeV had been applied at the particle level to the final state e+ and e−. In additionthe reconstructed e+e− pair was required to have an invariant mass in the range 2.7 - 3.1 GeV.

The results of applying cuts on the parameters R1 and R12 to the events in the signal and back-ground event samples are shown in Table 7-4. Looser TR cuts (R1 > 0.12, R12 > 0.15) were ap-plied in the barrel (|η| < 0.8) than in the end-cap region (R1 > 0.14, R12 > 0.18). These cutsreduce the trigger rate to 640 Hz. A breakdown of the type of pair combinations (hh, eh, ee)1

Figure 7-14 R1 vs R12 for e+e− pairs from J/ψ decaysin the end-cap region |η| > 0.8.

Figure 7-15 R1 vs R12 for eh or hh pairs (where ‘h’denotes a hadron) in the end-cap region |η| > 0.8.

Table 7-4 Efficiency for selecting the signal J/ψ → e+e− events and the trigger rate as a function of variousselection criteria: electron-pair identification (ID) using TR; pT cut and effective mass cut.

Cut(units are GeV)

SignalEfficiency (%)

Trigger Rate(Hz)

Background composition (%)

hh eh ee

No ee IDpT > 0.5

100 4000 97 3 0

Loose ee ID,pT > 0.5

77 640 19 60 21

Loose ee ID,pT > 0.5, M > 2

77 370 16 67 17

Loose ee ID,pT > 0.5, M > 2.5

77 300 16 66 18

Loose ee ID,pT > 1

65 220 15 59 26

Tight ee ID,pT > 0.5 M > 2

69 300 15 63 22

Tight ee ID,pT > 0.5, M > 2.5

69 250 15 62 23

0

0.2

0.4

0.6

0 0.2 0.4 0.6

R1

R12

Cut R1>0.14

Cut R12>0.18

0

0.2

0.4

0.6

0 0.2 0.4 0.6

R1

R12

Cut R1>0.14

Cut R12>0.18



contributing to the selected background events is shown in the table. It can be seen that the elec-tron identification cuts significantly reduce the number of triggers from hh combinations. Afterthe cuts, eh pairs dominate (60%). These results were obtained with a requirement for at least 9(out of a maximum of 11) hits in the precision layers. The efficiency for the signal is 77%. How-ever it should be noted that since similar requirements for electron identification and number ofprecision hits are imposed in offline analyses, only a small fraction of this loss should be la-belled as a trigger inefficiency. The cut on the number of precision hits is very effective in reduc-ing the trigger rate. With a looser cut of ≥7 (≥4) hits the trigger rate rises to 840 Hz (1.6 kHz).Applying a higher pT cut of > 1 GeV reduces the rate to 220 Hz for an efficiency of 65%.

The use of an effective mass cut at the trigger level was also considered. This would have theadvantage of preferentially selecting the events falling inside the mass window used in offlineanalysis. Applying a cut on the di-electron mass of M > 2 GeV, in addition to the loose electronidentification selection, reduced the trigger rate to 370 Hz without any additional loss of effi-ciency. If required, the trigger rate can be further reduced by applying the tighter electron iden-tification cuts (R1 > 0.14, R12 > 0.18) to the barrel region as well as to the end-cap. This gives areduction in trigger rate of ~20% with a loss of 10% of the signal.

It should be noted, however, that some simplification of the fitting procedure may be requiredin the trigger implementation, which may result in some degradation in resolution and loss ofefficiency. For example, if it proves not to be possible to correct for bremsstrahlung at Level-2,the signal efficiency would fall by 12%.

7.4.2 Inclusive D±s → φ π±

The selection for the channel relies on the reconstruction of the invariant mass ofthe φ from combinations of track pairs using a kaon hypothesis, and subsequently the Ds as thecombination of the φ candidate and one other track.

Trigger efficiency measurements were made on a signal sample of events withsubsequent decays and φ → K+K−. A cut of pT > 1.5 GeV was applied to the three fi-nal state tracks (K+K− π−) at the particle level.

The expected mass resolution for the reconstructed φ and Ds have been determined from a fullsimulation over the complete η range to be 3 MeV for the reconstructed φ meson and 15 MeVfor the Ds. The cuts |M(K+K−) − Mφ| < 30 MeV and |M(φπ) − MDs| < 150 MeV were defined soas to allow a 10σ window for the reconstructed mass. These mass windows are wider than thosewhich would be used in an offline analysis to allow for a possible degradation of resolutionwhich might result from simplifications in the algorithm required to meet the constraints for im-plementation within the trigger system.

The invariant mass cuts were applied to tracks with reconstructed pT > 0.5 GeV. This results inan efficiency for the signal of 94% at a trigger rate of 1.8 kHz (see Table 7-5). A reduction in trig-ger rate to 160 Hz can be achieved, without loss of signal, by raising the pT threshold for the re-constructed tracks to 1 GeV.

1. ‘h’ denotes a hadron - usually a π±.

Ds+− φπ+−→

Bs0

D→ s+−

π±

Ds+− φπ+−→



7.4.3 B0d → π+π−

The selection for the → π+π− channel relies on the application of pT cuts to the candidatepion tracks. This reduces the trigger rate by preferentially rejecting background processes,which have a relatively soft pT spectrum, whilst retaining the signal events which would beused in offline analysis. The efficiency measurements were made on a sample of → π+π−

events after the application of a cut of pT > 6 GeV to each final state π± and pT > 15 GeV to theπ+π− pair at the particle level.

Applying a cut to the reconstructed tracks of pT > 5 GeV gives a trigger rate of 540 Hz whilst re-taining 98% of the signal sample. A further reduction in the trigger rate to 250 Hz can beachieved without signal loss by demanding that the pT of the reconstructed candidate be> 10 GeV. An additional factor of ~2 reduction in rate is possible by requiring the invariant massof the candidate to be > 3 GeV. This results in a trigger rate of 130 Hz and an efficiency of98% for the signal (see Table 7-6).

Table 7-5 Selection efficiency for and trigger rate for various cuts.

Cuts (units are GeV) Signal Efficiency (%) Trigger rate (Hz)

pT > 0.5 100 4000

|ΔMφ| < 0.03, pT > 0.5 94 3100

|ΔMφ| < 0.03,|ΔMDs| < 0.15, pT > 0.5 94 1800

|ΔMφ| < 0.03, pT > 1 94 800

|ΔMφ| < 0.03, |ΔMDs| < 0.15, pT > 1 94 160

Table 7-6 Selection efficiency for → π+π− and trigger rate for various cuts.

Cuts (units are GeV) Signal efficiency (%) Trigger rate (Hz)

pT > 0.5 100 4000

pT > 5 98 540

pT > 5, pT(π+π−) > 10 98 250

pT > 5, pT(π+π−) > 10, M( ) > 3 98 130

Ds+− φπ+−→

Bd0

Bd0

Bd0

Bd0

Bd0

Bd0



7.5 Conclusions

It has been demonstrated that the required trigger performance for isolated high-pT tracks canbe achieved using simpler algorithms than those used for offline analysis. In particular no cor-rection procedure has been applied for bremsstrahlung losses. By requiring a track to be foundin both the precision tracker and TRT, and applying loose matching cuts between the measuredtrack parameters and those of the EM cluster, an acceptable Level-2 rate has been achieved forthe isolated high-pT electron trigger (700 Hz) with an efficiency of 88% for 30 GeV electronevents with pile-up. It is expected that a further reduction of trigger rate with respect to the re-sults shown here will be achieved by an optimisation of the selection cuts and when the full setof calorimetry information is included.

A preliminary study of three B-physics channels important for CP-violation studies and meas-urements of oscillations has demonstrated that the Inner Detector is capable of providing ahighly efficient selection for these channels. A key requirement is high efficiency for recon-structing tracks down to a pT ~ 0.5 GeV.

Implementation issues have not been addressed here. These are the subject of on-going studiesand will be dealt with in a trigger document which will be submitted at a later stage.

7.6 References

7-1 S. Sivoklokov et al., ATLAS Internal Note, INDET-NO-111.

7-2 R. Hawkings and A. Weidberg, ATLAS Internal Note, INDET-NO-052.

7-3 P. Eerola, ATLAS Internal Note, DAQ-NO-050.

7-4 I. Gavrilenko, ATLAS Internal Note, INDET-NO-016.

7-5 A. Dell’Acqua et al., ATLAS Internal Note, PHYS-NO-102.

Bs0


8 Conclusions on Performance 211

8 Conclusions on Performance

A great deal of new work has been done to study the performance of the Inner Detector layoutdescribed in this TDR. Overall, the performance appears to be well adapted to the physics re-quirements, although there remain some points of concern.

The current ATLAS software, in particular that written for the Inner Detector, allows sophisti-cated studies to be made, although, depending on the complexity of the study, the turn-roundtime can be quite lengthy. Considerable effort has been invested to ensure that the description ofthe detector is sufficiently precise and that all known effects1 which could influence the per-formance are included in the simulation. The work undertaken has benefited from the compari-son of results from several different pattern recognition programs.

8.1 Satisfaction of Specifications

The performance specifications for the ATLAS Inner Detector were set out in the beginning ofChapter 2 and have provided targets for the performance studies. In this section, a summary ofthe performance is provided. It is intended to be concise and indicative, consequently many ofthe details and caveats will be omitted. These were given in the preceding chapters of this re-port.

8.1.1 Basic Specifications

• With the B-layer, there are 3 pixel measurements, ≥ 4 pairs of Rφ-stereo measurementsand ~36 TRT measurements on tracks for |η| ≤ 2.5.

• The active volume of the Inner Detector contains a total of 43% of a radiation length and14% of an absorption length, averaged over |η| ≤ 2.5.

• The momentum resolution at high pT is σ(1/pT) ≈ 0.4 ΤeV-1 for |η| < 2, rising to 1.2 ΤeV-1

for |η| = 2.5. At low pT, the resolution is multiple scattering dominated around ~1.5%.

• The charge misidentification is < 2% and < 5% for 1 TeV muons and electrons, respec-tively.

• The angular resolution for high-pT tracks is σ(φ) ≈ 0.08 mrad and σ(θ) ≤ 1 mrad for|η| < 2.

• With the B-layer, the impact parameter resolutions (in μm) are σ(d0) ≈ 11 ⊕ 60/pT √sinθand σ(z0) ≈ 70 ⊕ 100/pT √sin3θ.

• The TR rejection is a complicated function of |η|, and to a lesser extent pT. For electronefficiencies of 90%, rejections of 10−103 (6−60) can be achieved at low (design) luminosity.

1. Except for some effects which will be the focus of on-going work.


212 8 Conclusions on Performance

8.1.2 Triggering Specifications

While the studies for trigger performance are still quite preliminary, the indication is that the In-ner Detector design will provide a satisfactory reduction in trigger rate, whilst maintaininggood efficiency for signal processes.

• For high-pT leptons, an efficiency of 88% can be achieved for a trigger rate of ~700 Hz.

• As examples of B-physics triggers, → J/ψ , inclusive B-decays withand → π+π− have been considered. The Level-2 trigger rates are less than ~250 Hz foreach process, with no loss of physics with respect to final analysis cuts.

8.1.3 Pattern Recognition Specifications

So far, no measurements made have been limited by pattern recognition problems, althoughthere is the indication that the merging of clusters in the B-layer is significant in the core ofhigh-pT jets (pT ~ 200 GeV).

• The track finding efficiency for isolated muons is > 99%.

• The track finding efficiency for isolated pions is > 85%, for pT > 1 GeV. At lower momen-ta, it is significantly affected by interactions with the material in the detector.

• The rate of fake tracks in pile-up is small and can readily be reduced below the rate fromreal pile-up tracks (2 × 10-2 in Δη × Δφ = 0.2 × 0.2, for pT > 2 GeV) by cutting on thenumber of hits on a track.

• Tracks in high-pT jets (pT ~ 200 GeV) can be reconstructed with efficiencies of ~88% andfake rates < 1%.

8.1.4 Physics Specifications

A large number of ‘building blocks’ for physics analysis have been examined. Performance con-sistent with the specifications has been observed and bodes well for physics at the LHC.

• Inclusive high-pT electrons (pT > 20 GeV) can be extracted from the background ofQCD-jets with an efficiency of 70% and a signal-to-background of ~5.

• Using low-pT electrons and combining the Inner Detector and EM calorimeter, b-jets canbe tagged with efficiencies of 50% × Br(b→eX) and gluon jet rejections of 100.

• Photons from H→γγ can be identified with 85% efficiency, while single electrons fromZ→e+e− can be removed with a rejection > 500.

• Photons from H→γγ which convert can be identified with 90% efficiency, while a rejectionof > 3 against π0’s can be achieved.

• ’s can be reconstructed with efficiencies of 75% up to a decay radius of 30 cm.

• The mass resolutions are 19 and 26 MeV for the muonic and electronic decays, respec-tively.

• For 50% b-tagging efficiency, rejections of ~80, ~40 and 8 against u-jets, gluon jets andc-jets, respectively, can be achieved for mH = 100 GeV.

Bd0

Ks0

Ds+− φπ+−→

Bd0

Ks0

Bd0


8 Conclusions on Performance 213

New studies for b-tagging have revealed that at higher energies (mH = 400 GeV) the rejection ofgluon jets is even more limited by gluon-splitting to heavy flavour than was found in previouswork [8-1] (mH = 100 GeV) - this is purely a physics issue. What is of more concern is the obser-vation that the rejection of light quark jets is limited by the creation of secondaries in the materi-al of the detector. Although it may prove possible to remove conversion electrons, interactingpions will prove more challenging.

8.2 Work to Do

While significant effort has gone into constructing an accurate model of the detector (detectorresponse and material) and the physics processes to which it will be subjected, work will contin-ue to obtain a better understanding of the following:

• The solenoidal magnetic field has not been extensively studied. The anticipation is that itwill not have a significant effect, except on pT resolution at high |η|, as discussed inSection 4.1.2.

• Systematics arising from misalignment have not been considered here, although thespecification for the alignment system is that such systematics should not significantlydegrade the track parameter resolution. This is discussed in Chapter 9 of this report.

• Work is needed to evaluate the robustness of the detector, in particular, to understand theconsequences of detector degradation (reduced efficiency and increased noise) arisingfrom irradiation.

For this report, a great deal of work has been undertaken to study topics closely related to phys-ics. Clearly, there is a need to continue this to achieve an even greater understanding. These top-ics include:

• Electron identification - to understand in more detail the jet rejection and study the con-sequences for high luminosity physics.

• Photon identification - to revisit the work contained in [8-3].

• b-tagging - to examine sources of degradation, optimisation of cuts and possible im-provements.

• Level-2 trigger - to consider a realistic implementation and to study in more detail globalLevel-2 and B-physics triggering.

In the light of the significant amount of material contained in the Inner Detector and the conse-quences for the physics accessible to the Inner Detector as well as the performance of the EMcalorimeter [8-2], work will commence to investigate:

• The consequences of the changes to the Layout which have occurred since September1996.

• The effects of reduced numbers of precision layers and whether satisfactory (or even im-proved) performance could be achieved with a lower material budget.

These points are very important but represent a large amount of work. Therefore, they will beconsidered in the context of those studies which are most likely to be significantly affected.


214 8 Conclusions on Performance

8.3 Summary

In the performance chapters of this TDR, it has been demonstrated that the current design of theATLAS Inner Detector satisfies the requirements for physics at the LHC. It is clear that the de-tector will play a central role in many key physics studies and will provide crucial informationfor extracting the maximal benefit from ATLAS as a whole.

8.4 References



8-3 S. Schuh et al., ATLAS Internal Note, PHYS-NO-070.


9 Alignment 215

9 Alignment

Alignment is the procedure in which the positions of the detector elements are determined. Theresidual uncertainties on these positions after the detector alignment has been performed aredefined as the detector misalignments. The alignment procedure for the Inner Detector is de-scribed in this Chapter. The alignment requirements are explained in Section 9.1, the overallalignment strategy is described in Section 9.2 and the details of the techniques used are given inSection 9.3.

9.1 Requirements

Any misalignment of the elements of the Inner Detector will degrade the resolutions of theoverall Inner Detector. Any significant deterioration of the intrinsic detector resolution due tomisalignment will degrade both the physics performance and the pattern recognition capabilityof the Inner Detector. Therefore the requirements for the alignment precision are set by de-manding that the overall effect of all misalignments of the Inner Detector should not significant-ly degrade the resolutions. For this analysis, a 20% degradation has been defined as significant.The resolutions assumed for the detector elements of the Inner Detector1 are given in Table 9-1below.

The requirements for the TRT are described in Section 9.1.1 and those for the SCT and the pixelsare described in Section 9.1.2.

9.1.1 Requirements for the TRT

The pT resolution of the overall Inner Detector at η = 0 and pT = 500 GeV with a beam constrainthas been calculated as a function of the resolution of the individual straws with the TRACKERRprogramme [9-1] and the results2 are shown in Figure 9-1. As explained in Section 9.3.6, the in-dividual straws can be aligned to a precision of 30 μm using the tracks found in the precision

1. The resolution assumed for the pixels is similar to the resolutions used in the performance studies dis-cussed in Section 3. However, it is planned to change the tilt angle of the pixels so as to maximise effi-ciency which will degrade the resolution slightly.

2. The pT resolution obtained is about 10% better than that obtained with the full detector simulation de-scribed in Section 3. However, the allowed module misalignments are very insensitive to this effect.

Table 9-1 Resolutions for the Inner Detector elements.

Element Resolution (μm)

TRT straws (low luminosity)(high luminosity)

170200

SCT strips 22

Pixels (Rφ) 10

Pixels (z) 50


216 9 Alignment

tracker, provided that the TRT is stable over periods of 24 hours. Such an additional 30 μm sys-tematic error gives a negligible contribution to the individual straw resolution.

However, to make a more conservative estimate of systematic effects, the TRT has been mod-elled as 4 “super-layers” and the misalignments are assumed to apply to the super-layers. ThepT resolution of the Inner Detector at η = 0 and pT = 500 GeV Monte Carlo has been calculatedas a function of the TRT super-layer precision and the results are shown in Figure 9-2. From acomparison of Figure 9-1 and Figure 9-2 one can see that a 70 μm resolution per super-layer isequivalent to a resolution of 170 μm per straw. The assumed alignment error of 30 μm was add-ed in quadruture to the intrinsic resolution of 70 μm. Therefore, the effective TRT super-layerresolution used in this analysis was 76 μm.

9.1.2 Requirements for the Pixels and SCT

The principle of the method used to determine the alignment requirements for the pixels andSCT was to use a Monte Carlo simulation in which the positions of the modules were moved byrandom Gaussian displacements from their nominal positions. The simulated hits were used toreconstruct tracks by a program that used the nominal module positions. The values of theGaussian errors were increased until the deterioration of one of the track parameters was equalto 20%. The track parameters that were used were the transverse momentum (pT), the two an-gles in spherical co-ordinates (θ and φ), the distance of closest approach (d0) to the beam lineand the corresponding co-ordinate along the beam direction (z0). For speed reasons a simpleMonte Carlo calculation was used rather than a full GEANT simulation but it was checked thatthe resolutions for the ideally aligned detector agreed between the two simulations [9-2].

The resolution of the tracker for pT = 100 GeV muons was studied as a function of the pixel andstrip module misalignment. In a first pass the alignment errors were assumed to be the same forthe pixel and strip modules. The resolutions as function of the misalignment error in the Rφ di-rection are shown in Figure 9-3. The values of the misalignment errors in all three dimensionswhich caused a 20% degradation in resolution are given in Table 9-2. However, this does not

Figure 9-1 Overall Inner Detector pT resolution as afunction of the individual straw resolution. The dottedline corresponds to a 20% degradation.

Figure 9-2 Overall Inner Detector pT resolution as afunction of the straw super-layer resolution. The dottedline corresponds to a 20% degradation.

16

18

20

22

24

200 250 300 350

Straw Resolution (μm)

σ(1/

p T)

for

p T =

500

GeV

(%

)

16

18

20

22

24

80 100 120 140 160

Super Layer Resolution (μm)

σ(1/

p T)

for

p T =

500

GeV

(%

)


9 Alignment 217

represent a realistic scenario because the alignment of the pixel detector is expected to be moreprecise than the SCT since it occupies a smaller volume. Therefore there is not a unique solutionto the problem of how large the misalignments can be before the resolutions are deteriorated by20%. In a second pass, misalignments were applied to either the pixel or the strip moduleswhile keeping the other sub-system perfectly aligned. The results of these studies are summa-rised in Table 9-3 and Table 9-4.

Figure 9-3 The resolutions of the Inner Detectors for pT = 100 GeV muons as a function of the module misalign-ment in the Rφ direction normalised to be 1 with no misalignment. The four η intervals are Barrel (B) 0-1.1, Over-lap (O) 1.1-1.6, Forward (F) 1.6-2.3, Far Forward(FF) 2.3-2.5.


218 9 Alignment

An iterative procedure was then used to determine a realistic set of alignment requirementswhich satisfied the 20% degradation rule. The conclusion of this study is that the module mis-alignments given in Table 9-5 approximately satisfy the requirements. The ratio of real (withmisalignment) to ideal (without misalignment) resolutions is given in Table 9-6 which showsthat this choice is satisfactory. More details of this optimisation procedure can be found in[9-2].

Table 9-2 Summary of the misalignments which caused a 20% degradation of the track parameter resolutions.In the cases marked ‘-’, the limit was not reached within the search range of 50 μm in Rφ and 1.5 mm in R and z.The four η intervals are Barrel (B) 0-1.1, Overlap (O) 1.1-1.6, Forward (F) 1.6-2.3, Far Forward(FF) 2.3-2.5.

Parameter

R error (μm) Z error (μm) Rφ error (μm)

B O F FF B O F FF B O F FF

pT - - - - - - - - 25 32 21 13

θ 90 31 41 65 60 60 120 320 16 18 22 22

φ - - - - - - - - 19 20 18 13

d0 - - - - - - - - 7 8 7 7

z0 75 27 37 60 50 50 120 250 19 21 21 19

Table 9-3 Summary of the misalignments which caused a 20% degradation of the track parameter resolutionsin the case of misaligned pixels only. The format is the same as for Table 9-2.

Parameter R error (μm) Z error (μm) Rφ error (μm)


pT - - - - - - - - - - - 22

θ 100 33 35 70 55 60 110 300 - - - -

φ - - - - - - - - - - - -

d0 - - - - - - - - 9 10 8 9

z0 70 27 33 50 52 47 105 250 - - - -

Table 9-4 Summary of the misalignments which caused a 20% degradation of the track parameter resolutionsin the case of misaligned SCT only. The format is the same as for Table 9-2.

Parameter R error (μm) Z error (μm) Rφ error (μm)


pT - - - - - - - - 30 30 25 20

θ 600 280 410 380 380 500 1300 - 17 19 21 15

φ - 700 - 700 1300 1300 - - 24 20 20 20

d0 - - - - - - - - 24 28 22 22

z0 750 320 500 400 470 600 - - 23 19 24 16


9 Alignment 219

9.2 Alignment Strategy

The ATLAS Inner Detector may not be sufficiently stable over short periods of time to rely en-tirely on alignment calculations based on tracks. This implies that more elaborate and automat-ed procedures are required. The strategy to achieve the required alignment precision for theSCT and the pixels is based on:

• measurements of prototype structures;

• initial X-ray survey;

• use of geodetic networks to create a run time survey;

• track- based alignment procedures.

For the case of the TRT an initial X-ray survey will also be performed as described inSection 12.5.1.5. The alignment requirements of the TRT are less severe than for the precisionlayers and therefore it will be possible to align the straws of the TRT with tracks found in theprecision layers (see Section 9.3.6).

9.2.1 Measurements of Prototype Structures

Measurements of the deformations of prototypes of the overall structure and the individualmodules will be made under thermal and mechanical loads. Electronic Speckle Pattern Interfer-ometry (ESPI) will be used for these studies (see Section 9.3.1). These measurements will beused to optimise the design, to minimise deformations, and to calibrate the FEA programs thatare used to estimate the expected distortions.

Table 9-5 Allowed module misalignments for the pixels and SCT.

Module R error (μm) Z error (μm) Rφ error (μm)

Pixel B-layer 10 20 7

Pixel barrel 20 20 7

Pixel wheels 20 100 7

SCT barrel 100 50 12

SCT wheels 50 200 12

Table 9-6 Ratio of resolutions with and without misalignment, for the four η intervals defined in Table 9-2.

Parameter Barrel Overlap Forward Far Forward

pT 1.09 1.08 1.08 1.11

θ 1.13 1.22 1.21 1.13

φ 1.09 1.11 1.11 1.11

d0 1.20 1.21 1.23 1.25

z0 1.12 1.25 1.17 1.12


220 9 Alignment

9.2.2 Initial X-Ray Survey

The silicon detectors are sensitive to X-rays. Therefore, by sending beams of X-rays through theSCT, the positions of the strips can be determined during the assembly of the SCT. The X-raysurvey of the SCT is described in Section 9.3.2.

9.2.3 Geodetic Grids

The measurement techniques applicable to real time surveying of a particle detector generallymake one-, two- or three-dimensional measurements at a number of localised positions withinthe structure. In order to produce a consistent, distributed survey of detector element positionsacross the Inner Detector, it will be necessary to combine a large number of measurements. Oneway to achieve this is by configuring the measurements as a three-dimensional geodetic net-work - a network of geometric measurements made between pairs of points (nodes) with eachnode being in general common to several measurements. The numerical majority of the meas-urements made in the SCT/pixel survey system will be based on 1D length measurementsmade using Frequency Scan Interferometry (FSI) as explained in Section 9.3.4. In addition, it isforeseen that Straightness Monitors (SM), see Section 9.3.5, will be used in the situations wherethis technology is most suitable, namely detection of motions transverse to a defined axis. Sucha hybrid system offers robustness, reduction of systematic errors and assignment of each type ofmeasurement to the most suitable technique. The design of the geodetic grids is discussed inSection 9.3.3.

Finite element analysis (FEA) and laboratory measurements of the behaviour of modules andsupport structures under thermal and mechanical loads will provide a parametrisation of theirdeformation modes. Thus, by monitoring the movement of a large number of selected referencepoints in the Inner Detector, it will be possible to infer the positions of individual detector ele-ments by interpolation.

9.2.4 Track-Based Alignment Procedures

Although there will not be complete reliance on track-based alignment procedures the largerates of high pT muons will enable the use of track-based alignment procedures to verify the au-tomatic survey techniques and to provide the ultimate precision alignment constants (seeSection 9.3.6).


9 Alignment 221

9.3 Techniques

The techniques that are required by the alignment strategy outlined in Section 9.2 are describedin this section.

9.3.1 Electronic Speckle Pattern Interferometry

9.3.1.1 Introduction

Electronic Speckle Pattern Interferometry (ESPI), also known as ‘TV Holography’, is a laserinterferometric technique for visualising micron-scale displacements on the surfaces of ‘normal’objects (that is, objects with optically rough surfaces) [9-3], [9-4].

In the context of the ATLAS Inner Tracker, ESPI is being used as a development tool to help un-derstand the detailed behaviour of the complex mechanical structures which will support theindividual detector elements. These support structures vary in scale from individual modules tocomplete barrels and discs and will ultimately determine the exact position and orientation ofevery silicon detector strip and pixel. It is therefore essential to have an accurate knowledge ofthe way these structures distort under realistic operating conditions. This is particularly impor-tant in view of the planned extensive use of exotic materials (such as the so-called ‘zero’ thermalexpansion carbon-fibre composites) to minimise the material in the tracker. The existing data onthe mechanical and thermal properties of these new materials are often incomplete or unrelia-ble, particularly at the unusually low stresses and displacements that are relevant to the ATLASInner Detector.

An improved understanding of these structures and materials will allow more accurate compu-ter models to be devised to predict the mechanical behaviour of the tracker during operation.Such models will help in the understanding and correction of alignment errors when analysingthe physics data. This will be necessary because, for example, there are likely to be temperaturechanges inside the tracker, during normal operation and particularly as a result of any partialfailure of the electronics or cooling systems.

It will also be essential to understand the deformations of the support structures during the as-sembly and installation phases. This will be particularly important when a large component(such as a barrel) is only partially loaded with modules and will therefore not have taken up itsfinal deformed shape.

ESPI can measure surface deflections in the range of about 1 - 100 μm, under both static and dy-namic conditions, with a typical resolution of better than 1 μm. Applications include studies ofdeformations as a result of mechanical loading, thermal distortions and vibration analysis. Itcan be used to measure displacements both within the plane of the object’s surface, along anychosen axis, or perpendicular to this plane. The size of objects that can be studied varies over alarge range, from a few millimetres to a large fraction of a metre. The principle limitation forlarge objects is the total laser power available. The system presently in use is based around astandard ‘small-frame’ argon ion laser, with a single frequency output of just under 1 W at 514nm (in the green).

Unlike other interferometric techniques, there are few restrictions on the optical properties ofthe surface being visualised. In particular, it does not have to be optically flat, or maintained atsome precise angle. ESPI will work with any diffusely reflecting surface, provided that suffi-


222 9 Alignment

cient light is scattered back towards the camera. In the case of black surfaces (such as the car-bon- fibre composites mentioned above) it is necessary to increase the amount of light returnedto the camera by spraying the surface with a thin layer of white powder, similar to chalk dust.The theory of ESPI is explained in detail in Refs. [9-3] and [9-4].

9.3.1.2 Experimental Method

Figure 9-4 shows schematically a typical experimental set-up for measuring ‘out-of-plane’ dis-placements. For flexibility and ease of setting up, the object under test is illuminated via a single

Figure 9-4 Schematic diagram of the ESPI set-up.


9 Alignment 223

mode optical fibre, with diverging optics permanently attached to its output end. This generatesa laser speckle pattern which is imaged by the lens onto the CCD array in the modified videocamera. Although the intensity of this speckle pattern varies randomly across the CCD, the am-plitude and phase of each speckle are well defined and constant, provided that the object is sta-tionary. A small fraction of the laser light is split off to form a reference beam, which is deliveredvia an identical optical fibre and a beam splitter directly onto the CCD. Using the variable atten-uator, the reference beam intensity is adjusted to be approximately equal to the average intensi-ty of the speckle pattern. The reference beam, which also has a constant amplitude and phase,interferes with the speckle pattern. Thus the intensity falling on the CCD is related to both theamplitude and phase of the light scattered by the corresponding region on the object. For an ob-ject with approximately uniform reflectivity, the phase of each speckle has effectively been en-coded as a variation in its intensity on the CCD pixels.

If two frames are recorded, before and afterthe object has undergone some displacement,and the two images are subtracted, a set of ‘in-tensity correlation fringes’ is generated.Figure 9-5 shows a typical series of such fringepatterns, generated by heating a silicon detec-tor bonded to a pair of narrow carbon-fibrebeams [9-4].

Any part of the object’s surface which movestowards or away from the camera bybetween the two frames (where N is an integerand is the laser wavelength) leads to achange of in the optical phase of the cor-responding speckles in the image, whichtherefore have the same intensity in bothframes. This results in a black region in thesubtracted frame, regardless of their originalintensity. Any intermediate value of surface displacement, and hence optical phase change, re-sults in an intensity that depends on both the original amplitude and phase of the correspond-ing speckles. Thus, a set of dark fringes is formed across the subtracted frame. Each dark fringerepresents a contour of constant ‘out of plane’ displacement of the object’s surface, with a con-tour spacing of (i.e. 0.25 μm for the argon ion laser). This provides a measurement of themotions of the object towards or away from the camera (‘out-of-plane’ displacements). An alter-native arrangement, in which the object is illuminated by beams from a pair of matched fibresand the reference beam is not used, allows measurements of displacements in the plane of thesurface of the object (see Figure 9-4).

Using the simple approach described above, it is not possible to resolve the ambiguity betweendisplacements towards or away from the camera. However this can be done by using a slightlymore complex method, known as ‘phase stepping’ [9-5]. In many cases, the additional complex-ity of phase-stepping is not justified, as the direction of motion can be deduced from priorknowledge of the physical properties of the object (for example, an increase in length due to anincrease in temperature).

An important practical aspect of making ESPI measurements is the requirement to distort theobject under test in a controlled way. This involves either changing the temperature in an envi-ronmental chamber, mechanically loading or vibrating the object under test. A large glass front-ed environmental chamber has been designed and built as part of the ESPI facility for studying

Figure 9-5 Series of ESPI fringes obtained by heatinga silicon detector.

N λ 2⁄( )

λ2Nπ

λ 2⁄


224 9 Alignment

small and medium sized components (such as modules and local supports). This chamber isequipped with module cooling and thermometry systems, and is capable of operation between

and about .

An entire ‘cold room’ is under construction for working on larger objects (such as complete bar-rels). This has a floor of 7m x 3.5m, a height of 3m, with a cooled 5m x 1.5m vibration isolatedoptical table.

9.3.1.3 Typical Examples of ESPI in the ATLAS SCT

Evaluation of Module DesignsAn important aspect of any module design is thermo-mechanical distortion, both as a result ofcooling it from room temperature to the SCT operating temperature (of about ) and as aresult of internal temperature gradients generated by detector heating and the electronics/cool-ing systems. In order to asses the suitability of different module designs, it has been necessaryto measure the thermo-mechanical performance of several prototype modules in the environ-mental chamber. Figure 9-6(a) depicts an early example of such a prototype module, seenthrough the ESPI camera (with the reference beam turned off). Figure 9-6(b) shows the interfer-ence pattern that was generated by cooling the ambient temperature by . Each fringe repre-sents a change in out-of-plane displacement of 0.25 μm. The large number of fringes shows thatthis early design suffered from significant thermo-mechanical distortions, due mainly to the useof materials with mismatched thermal expansion coefficients. Through a careful choice of mate-rials and the use of symmetry in the design, as a result of the lessons learnt during these (andother) measurements on the early prototypes, later designs have performed much better thanthis (see Section 11.5 for details).

Figure 9-6 (a) Early prototype SCT module. (b) ESPI fringes generated by a change in the module temperatureof 1 °C.

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9 Alignment 225

Materials and Support StructuresA series of measurements have been made of the thermal expansion coefficient of a variety ofcarbon-fibre plates, tubes and beams. A series of ESPI measurements will be made on proto-types of local supports, a complete carbon-carbon-fibre cylinder and a complete forward disk.Investigations of the prototype local supports will include static loading and vibration studies,measurements of the thermal expansion coefficients, checking for twisting and other more com-plex distortions as the temperature is changed. It is also planned to investigate the effect of run-ning several overlapping dummy thermal modules simultaneously, complete with simulateddetector and chip heating and a full cooling system. Investigations of the carbon-fibre cylinderwill include static loading, thermal expansion studies and vibration measurements. A similarset of measurements is also planned for the prototype disk structure.

9.3.2 Initial Survey with X-Rays

The positions of detector strips (SCT) and straws (TRT) will be measured before installation ofthe Inner Detector inside ATLAS. The measurements are difficult to do with the required preci-sion, particularly after the barrels are brought together into the final assembled structure. A par-ticularly elegant and cost-effective method to accomplish such surveys is to use X-ray beams.These are directed through the layers of the detector, which are themselves used to locate wherethey penetrate the detector. By careful design of the mechanical components of the X-ray sourceand appropriate choice of the X-ray energy and collimation, it is possible to produce a systemthat will allow accurate surveys of all detectors in a reasonable time period.

The X-ray calibration stand for the TRT is described in Section 12.5.1.5 and the equivalent sys-tem for the SCT is described in Section 9.3.2.1 below. The use of an X-ray scanner for the pixeldetector is under consideration.

9.3.2.1 SCT

This section describes the system to perform the X-ray survey of the SCT and results from pro-totype tests. Such a system is also useful during assembly of the barrel structures. Considerableprogress has already been made in the implementation of the system, a collimated beam hasbeen built and the residuals of the measurements of silicon strip locations measured. The effectof the amount of material in the beam has been studied and the design requirements of the finalsystem have been evaluated. The ATLAS front-end electronics has been designed with a modeintended to allow the detection of X-rays in a survey mode. This section describes the work todate and the final system envisioned.

9.3.2.2 X-Ray Source

The X-ray source is based on two commercially available components:

• a fine-focus spot X-ray tube (spot size= 0.2-0.4 · 8 mm2; E = 10 - 40keV; P ≤ 2kW);

• high-accuracy and resolution translation and rotational stages (1 - 5 μm for lengths up toa few metres and 1” in the range 0 to 360°.

The low wavelength of the photons (10 - 50 pm) allows production of very narrow beams with-out problems from diffraction. The divergence of the beam can be kept low enough (40”) usingcollimating slits. Such beams have been in use for more than two years for investigation of the


226 9 Alignment

MDT and TRT in ATLAS [9-7]. The X-ray tube produces a beam spot on the target which is ap-proximately 1 mm in diameter. This is viewed at a very shallow angle (approximately 3°),which causes the apparent spot size to be small in one dimension. The direction and divergenceof the X-ray beam is then controlled by use of a collimation system which has at least two colli-mator slits separated by a distance of order tens of centimetres. A prototype source for use withthe SCT was developed to determine if adequate divergence, beam size and intensity could beachieved. It was also checked that the centroid of the beam did not move as the beam passedthrough increasing quantities of material, which would be the case if the energy profile acrossthe beam was asymmetric). Figure 9-7 is a schematic of the set-up used.

Figure 9-8 (a) shows the measured hit location of the X-ray beam on a silicon detector as a func-tion of the position of the detector on a translation stage and Figure 9-8(b) shows the residualsassociated with the measurement. The RMS of the residual distribution is a measure of the accu-racy of the X-ray beam location with respect to the silicon detector.

Figure 9-9 shows the X-ray beam location as a function of the quantity of aluminium sheetplaced in front of the detector. The RMS of the residual distribution is only 2 μm which showsthat there is no significant effect from varying the absorber thickness. Table 9-7 characterises theresults achieved.

Figure 9-7 X-ray scanner test set-up. A computer-controlled high precision trasnlation stage moves the siliconmodule across the X-ray beam.

ATLAS-SCT


9 Alignment 227

9.3.2.3 Measurement System

Several different schemes have been consid-ered for the geometry of the mechanical sys-tem used to mount the X-ray source and allowsurvey. The TRT system uses a polar scanner.This has the virtue of being ‘projective’ in thesense that the X-rays follow trajectories closeto those which would be followed by high en-ergy particles during data taking. This is anappropriate geometry for the forward SCTsystem. For the barrel region, a cylindricalscanning scheme is proposed. Two beams aregenerated eccentrically relative to the axis of arotation stage, which is itself translated linear-ly along the z axis of the barrel structure. Theprinciple of the stereo reconstruction is shownin Figure 9-10 and Figure 9-11 shows the pro-posed arrangement. During a single rotationof the X-ray sources, at fixed z, each silicon module will be scanned twice; but with a differentbeam direction each time. This dual measurement allows calculation of R and φ for each ele-ment of the module using the stereo information.

The accuracy of the system is based on the rotation stage in the case of R and φ. The selectedstage [9-8] has a an accuracy of 1”. The x and y location of the rotation stage are also required tobe known to high precision and this is established by use of optically transparent silicon detec-tors sitting on collimated laser beams which run along the z-direction. The z-position of thestage is measured using standard optical interferometric fringe-counting relative to a definedstart position. Certain elements of the mechanics must be inherently stable (for example the col-limation slit mounting plate). It is planned to use zero CTE carbon composites for such parts.

Figure 9-8 (a) Measured silicon hit locations as afunction of the translation stage position (b) distribu-tion of hit residuals.

Figure 9-9 X-ray beam location as a function of thethickness of aluminium sheet in front of the silicondetector.

Figure 9-10 Principle of geometry of SCT X-ray sur-vey.

SCT


228 9 Alignment

The structure must also be highly rigid and immune to vibration. It is anticipated that the finaldesign will be quite massive.

For the forward SCT regions, X-ray survey of individual wheels is not anticipated. This is be-cause they are essentially flat surfaces which are well adapted to survey by standard opticalmethods. The primary function of the X-ray system in the forward region will be for survey ofthe ensemble of disks after assembly into the space-frames.

9.3.2.4 SCT X-ray Survey Accuracy

Using reasonable assumptions about the various errors that will be unavoidable in the system,it has been calculated to what precision the elements of the barrels may be measured. These arelisted in Table 9-8.

This precision matches the precision with which it is required to know the location of the ele-ments as specified in Section 9.1. For these measurements to be meaningful, it is clear that the fi-nal survey must be on the assembled structure with all loads in place. The system is designed tofit down the middle of the assembled detector (in the absence of the pixel detector). Providedthat the mounting points are kinematic it should be possible to produce a highly accurate sur-vey of the powered, cooled detector. Any motions caused by a different distribution of load af-ter installation in the experiment should be of a global nature; an overall twist for example. This

a. Limited by detector pitch, multiple strips must be hit in order to be able to form a centroid. The collima-tion system can deliver narrower beams than are useful.

Table 9-7 Parameters of the SCT prototype x-ray survey system.

Quantity Value

Energy range 10 keV - 40 keV

Mean energy 27 keV

Thickness of silicon beam can penetrate 15 mm

Width of beam 50 μma

Divergence 200 μrad

Beam intensity out of collimators 106 X-rays/s

Counting rate in 300 μm thick silicon 4 104 X-rays/s

Accuracy of measurement (analogue read-out) 2 μm

Centroid motion with material penetration < 4 μm after 1.2cm of aluminium

Table 9-8 Projected SCT X-ray survey accuracy.

Dimension Accuracy

z 40 μm

R 50 μm

R φ 7 μm


9 Alignment 229

type of motion is well monitored by the FSI system, which also forms part of the overall align-ment and survey strategy. The X-ray survey will be optimised based on the studies of the firstbarrel. After X-ray survey of the individual barrel(s) has been performed, the entire X-ray sur-vey system will be moved to CERN, where it will be used to survey the four barrels when theyare installed in the surface building above the pit. This X-ray survey may also be used to simul-taneously survey a sub-sample of the TRT wires relative to the SCT. After surveying the barreldetectors, the delivery system will be modified to perform a projective survey of the forwarddetectors. This adaptation is not yet designed, but will be based on the same precision rotationstage as the barrel system. The stage will be arranged to rotate around the beam-axis direction.A mounting fixture will be attached to the stage, perpendicular to the stage surface. The sourcemounting plate will be re-attached to the stage on the perpendicular mounting fixture, such thatone beam originates radially from the rotation axis. By rotating the source on the fixture, θ canbe adjusted, with the φ direction controlled by the rotation stage.

The FSI system (see Section 9.3.4) will be operated simultaneously with the X-ray survey systemin order to calibrate the FSI measurements.

9.3.3 Geodetic Grids


In the SCT and pixel survey system, many measurements made using the FSI and straightnessmonitor techniques will be combined using a highly over-constrained, three-dimensional geo-detic network. Each node on the network is a 3-dimensional point and its location therefore in-

Figure 9-11 Proposed X-ray measurement system.


230 9 Alignment

volves three degrees of freedom. Hence, at least three 1D measurements are required for eachnode. To have a robust network more than three measurements should be made to each point.The networks will be based on 1D length measurements using FSI. In addition to this, straight-ness monitors will be used in the forward SCT grid. Each node of the FSI network, called a jewel(see Section 9.3.4.3) will be used to make length measurements to several other jewels. In addi-tion to permitting the calculation of the locations of the nodes in three dimensions, such a net-work will allow internal cross-checking of the measurement data in order to identifymeasurement biases caused by measurement mistakes (such as miscounted fringes) and local-ised gas refractive index changes (see Section 9.3.4). In order to use the grid data, an initial cali-bration will be required to measure the positions of the nodes relative to the SCT supportstructure.

The complexity of the survey requirements and the small margin between the intrinsic meas-urement precision of suitable techniques and the required precision mean that careful optimisa-tion of the configuration of the network is necessary. A suitable network will permitdetermination of the node locations with the required precision, and will satisfy a number ofquality (or reliability) criteria defined below. In addition, there are experimental requirementswhich must be met, such as robustness with respect to loss of measurement channels.

9.3.3.2 Network Design

PrecisionThe physical requirements for the precision of the SCT and pixel survey system are given inSection 9.1.2. The requirements are most stringent in the Rφ direction. Taking into account thepositioning tolerances of the FSI jewels (see Section 9.3.4.3) and the errors arising from the inter-polation between the jewels and the detector elements, the Rφ precision required from the geo-detic network itself will be about 5 μm. In practice, it is found that suitable networks will havecomparable precisions in all three directions, and so the weaker R and Z specifications will bemet comfortably by any network meeting the Rφ requirement.

Network ReliabilityA measurement which for any reason has a value incompatible with its expected mean andstandard deviation is said to have a bias. The redundancy of a geodetic network allows somebias detection capability as well as a degree of insensitivity to undetected biases. These arequantified for each particular measurement as the Minimum Detectable Bias (MDB) and the Bi-as-to-Noise Ratio (BNR) (see [9-11] for further discussion).

A possible FSI measurement bias is that a fringe is missed in the counting process (seeSection 9.3.4). This is most likely to occur for the longer measured lengths where both the fringeseparation and the signal-to-noise ratio will be lowest. A counting error of one fringe wouldcause a bias of 50 μm in the length measurement. Thus with a minimum detectable bias of<50 μm, at a confidence level of 99.9% for all measurements, it would be likely that any singlefringe counting error in an FSI data set of ~500 measurements would be detected during thedata analysis.

Another possible source of a measurement bias is a localised change in the refractive index ofthe gaseous medium due to an undetected hot- or cold-spot. A change in the path-averagedtemperature of 0.1°C would cause a 0.1 ppm change in the refractive index, and since the meas-ured length is inversely proportional to the value of the refractive index, this would result in a0.1 ppm measurement bias. There is no lower limit to the MDB requirement which would be de-


9 Alignment 231

rived from considering this type of bias. It is expected that the gas flow rate and mixing will besufficient to make any index-induced errors small compared to the desired accuracy.

9.3.3.3 Barrel SCT and Pixel Alignment Networks

It will most likely be difficult to make survey measurements in the transition region betweenthe barrel and the end caps and it is foreseen that only a limited number of FSI length measure-ments will be possible between the barrels and the end-caps. The barrel and the two end capswill thus have three independent geodetic survey networks. These individual networks willthen be linked together by means of a relatively simple analysis of tracking data and the use ofthe FSI measurements between the three regions.

Application of survey techniques to the SCT barrel is complicated by the presence of the SCTservices and the small amount of space in the end planes and between the cylinders. There willbe space available to make FSI measurements in two 10 mm thick planes between the two endsof the barrels and the interlink plates. It is expected that the FSI “jewels” (described inSection 9.3.4.3) will occupy a volume of no more than 1 cm3.

Longitudinal measurements from one cylinder to another through the gap between planes maybe made with FSI or with transparent silicon straightness monitors. The thickness of the mod-ules and cylinders, in addition to restricting the space available for making survey measure-ments, may make it necessary for the jewels to span the ends of cylinders or disks so thatmeasurements can be made to both sides.

A possible layout of the transverse survey network for the barrel SCT is shown in Figure 9-12. Apreliminary design for the pixel barrel network is shown in Figure 9-13. Only the transversenetwork at the end of the detectors is shown. The design of the longitudinal networks is understudy but a previous analysis of a longitudinal network showed that the required longitudinalprecision would be achieved by any reasonable network [9-11] that had sufficient transverseprecision.

Figure 9-12 Geodetic alignment network for the barrel SCT detector. Only part of the network is shown for clar-ity.


232 9 Alignment

9.3.3.4 Forward SCT Alignment Networks

Sight lines in the forward region are readily available. The forward survey measurements willbe made primarily using the FSI technique, with the addition of straightness monitors for meas-urements to determine rotations of the disks about the beam axis. A 2D representation of a pos-sible layout of the forward alignment network for the SCT disks is shown in Figure 9-14.Even-numbered disks have three ‘inner’ FSI jewels positioned at their inner radius on the sidecloser to the interaction point at φ = 0˚, 120˚, 240˚, and three ‘outer’ jewels positioned on the op-posite side at R= 500 mm and φ = 60˚, 180˚, 300˚. Odd-numbered disks have the same arrange-ment of jewels but rotated by Δφ = 30˚. This rotation is necessary in order to prevent some of thesight lines from crossing the beam pipe.

FSI length measurements are made from each inner jewel to the other two inner jewels on thesame disk and to the inner jewels on both the preceding and the following disks. This results inan over-constrained grid in which each jewel can lose one of its measurements and still be fullyconstrained. Each outer jewel of disk N is connected by measurement lines to the three innerjewels of disk N+1. Straightness monitors (described in Section 9.3.5) utilise lines of sight alongthe inner edges of the disks to measure the rotations of disks in φ as illustrated in Figure 9-14.

9.3.3.5 Network Precision Calculations

The SCAN-3 network analysis program [9-12] has been used to evaluate the precision and relia-bility of networks of the types envisaged for the alignment system for the SCT and pixel detec-tors.

Figure 9-13 Geodetic alignment network for the barrel pixel detector (preliminary).

R=10.5cm

R=4.7cm

R=13.7cm


9 Alignment 233

The calculation of the node locations (and their precisions) from the measurement data requiresthat two points in the network be constrained to determine the position and orientation of thewhole network within a coordinate system. An appropriate figure of merit for a network is thepositional precision for the node which is least well determined (in a given direction) with re-spect to the chosen coordinate system. This ‘worst node’ is in a certain sense the node furthestfrom the constrained nodes. In Table 9-9 the worst-node precisions in each of three orthogonaldirections are given for the networks shown in Figure 9-12, Figure 9-13 and Figure 9-14. For-ward SCT networks were studied both with and without straightness monitors. In networks inwhich FSI measurements are combined with straightness measurements, an additional errorarises in the combination of the two sub-networks. It has been shown that with even a conserv-ative estimate of this error, the use of straightness monitors for longitudinal measurements (i.e.with laser beams parallel to the beam axis) is desirable for achieving the necessary precision inthe transverse coordinates. A similar complexity forward network without the use of straight-ness monitors has a worst-node Rφ precision which is a factor 3 to 4 worse than the require-ments. From Table 9-9 it can be seen that the requirements can be met if a precision of 1 μm forthe FSI length measurements can be achieved.

9.3.3.6 Additional Requirements

Due to shut-downs and maintenance, continuous operation of the survey system is likely to beimpossible. Many existing metrological techniques are only capable of monitoring variations inposition and are therefore ruled out by this requirement. As for any system used in ATLAS, thein-detector elements must have low radiation length, very low mass, small physical size, mustbe radiation hard and must require no maintenance or adjustment during operation. These re-quirements are satisfied by both the proposed techniques (FSI and SM).

Figure 9-14 Geodetic alignment network for the forward SCT. The measurements along the inner edges of thedisks are made using straightness monitors (shown as dashed lines). All other measurements are made usingFSI (shown as thick solid lines).


234 9 Alignment

9.3.4 Frequency Scan Interferometry


Frequency Scan Interferometry (FSI) is an interferometric length measurement technique underdevelopment for ATLAS [9-9], [9-10], [9-11]. Its virtues are:

• high precision (≤1 μm) absolute length measurements which does not require any movingpieces.

• no active devices are required on the detector.

• components on the detector are radiation hard and have very low mass.

• small additional cost for adding extra measurements.

9.3.4.2 Basic Principles of FSI

FSI works by counting interference fringes in a remote, fixed path length, self-aligned,two-beam interferometer as the laser frequencies is scanned. This scan actually takes the form ofa series of sub-scans, each of around 30GHz, separated by much larger gaps. These sub-scansare linked together over a total range of about one percent of the laser’s wavelength, which inthis case is in the near infra-red at around 800nm. A laser linewidth of less than 1MHz is re-quired to meet the basic precision of ≤1 μm over a measured length of one metre, set by thespecification for the geodetic grids described in Section 9.3.3. It is the recent commercial availa-bility of high performance tunable lasers that has made FSI a viable technique.

A single FSI interferometer is required for each length measurement, but many interferometerscan share the same tunable laser and frequency measurement equipment that lie at the heart ofthe system. Since these latter two items dominate the cost of an FSI system, the technique is wellsuited to the present requirement for many simultaneous length measurements.

The basic concept is illustrated schematically in Figure 9-15, which depicts an individual inter-ferometer, together with the shared laser and frequency measurement system. Each interferom-eter will be constructed from a pair of millimetre-size objects and will have very low mass, nomoving parts, no active components and will require no precise adjustment for the interferom-

Table 9-9 Results of SCAN-3 network precision calculations. Precisions are given as multiples of the FSI preci-sion (≤ 1 μm).

Worst nodeRφ precision

Worst noderadial precision

Worst nodez precision

Barrel pixel 4.3 5.3 N/A (2D network)

Barrel SCT 9.0 7.0 N/A (2D network)

Forward SCT withlow precision SM-FSIlink

6.5 6.5 7.4

Forward SCT withhigh precision SM-FSIlink

3.5 3.2 7.3


9 Alignment 235

etry to work. A pair of single-mode, radiation hard fibres will be used to enable remote opera-tion, one for illumination of the interferometer and the other for detection of the resulting fringepattern. All paths in fibre are common to both beams, so that phase and polarisation errors in-troduced by the fibres will not appear in the interference signal.

The use of fibres with bare polished ends (i.e. with no optics attached) not only minimises themass, but greatly simplifies interferometer construction. Also, the angular divergence (of the or-der of 5 °) of the light coupling out of and into the fibres and the use of a retro-reflector minimis-es the pre-alignment requirements during assembly. However an initial calibration of thesystem will be necessary to measure the precise location of the retro-reflectors relative to thesupport structure. Since only a small fraction of the light is accepted by the return fibre, the pho-todetector therefore has to be a sensitive photon-counting device. In each interferometer, themeasured length is between a known point near to the closely positioned ends of the two fibresand the corner point of the retro-reflector. A single interferometer design is expected to be capa-ble of making measurements in the range of ~ 10 cm to ~ 1.5 m. Because a single laser will beshared between several interferometers, groups of length measurements can be made simulta-neously as indicated in Figure 9-16. All the complex optical equipment, including the laser, pho-todetectors and wavelength measurement system will be located at the surface facility, wherethey will be accessible for maintenance.

The control system, the data acquisition and the geometrical analysis will be automated to pro-vide a continuous quasi-real-time survey of the detector with minimal human intervention.Since it measurements absolute distances, the system may be powered down at any time with-out penalty.

It is possible that there could be mechanical vibrations within the Inner Detector during opera-tion. If no precautions were made for rejecting vibrations, an oscillation of the interferometerlength with an amplitude greater than half the laser wavelength would result in a loss of thefringe signal. Smaller vibrations would reduce the possible measurement precision. The criticaldependence of the measurement precision upon the phase accuracy and the possibility that thesignal could be rendered useless by the presence of vibrations with an amplitude smaller thanthe required measurement precision have led to the development of a vibration rejection tech-nique based on adding a fast optical frequency jitter to the relatively slow monotonic FSI scan.This should result in immunity to vibrations with a frequency of up to 100 Hz and an amplitudeof up to 1 μm.

Figure 9-15 The FSI interferometer. The use of a retro-reflector means that prealignment of the optics is notnecessary.

LOCATION

ATLASOUTSIDE

ACCESSIBLE

beamsplitter

measured length

PASSIVE FIXED-PATH INTERFEROMETER

return fibre

retroreflector

delivery fibre

I N S I D E A T L A S

DETECTOR

LASERTUNABLE

FREQ.MEAS.


236 9 Alignment

9.3.4.3 Jewels

The term jewel is used to describe the object that resides at a node in the FSI system. A singleFSI interferometer is comprised of two basic components: an integrated fibre pair and beam-splitter arrangement at one end and a retro-reflector at the other end. A jewel is therefore a com-bination of several of these components in a single integrated object. Some nodes in the forwardSCT grid require as many as eleven separate components, typically four fibre pair/beamsplit-ters and seven retro-reflectors. Work on the detailed development and prototyping is still inprogress. However, the basic design described here is expected to prove satisfactory.

The first component, the fibre pair/beam split-ter, consists of a pair of single-mode radiationhard optical fibres (with a core diameter oftypically 5 microns and overall cladding diam-eter of 125 microns) epoxy-bonded into a pre-cision ferrule. The ends will then be polishedat an angle to eliminate internal reflectionsback along the fibres. The beamsplitter will beformed onto the polished end of the ferrule,by bonding on a thin, anti-reflection coatedlayer of glass. The second component of a jew-el is the retro-reflector, which is presently en-visaged to be an internal glass corner cube.This has the advantage of ease of manufactureand mechanical stability. If there proves to be aproblem with radiation hardness of the glass,then the alternative of a moulded and meat-plated external retro-reflector will be consid-ered. The accuracy requirements for the retro-reflector are not expected to be very critical, sinceonly a very small fraction of the returning wavefront will be intercepted by the receive fibre.

A modular approach to the construction of complete jewels from the two components describedabove is being developed. Two sub-elements have been designed and are currently being proto-

Figure 9-16 The FSI system. All the complex optical equipment is external to the detector.

frequency measurement

A2

A3

A4

A5

A1

B1

B2

B3

B4

B5

C1

C2

C3

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D1

D2

D3

D4

D5

RECEIVE

SEND

laser beam

fibre heads

COMPUTER

LASERTUNABLE

ADCs & COUNTERS

d1 d2 d3

optical multiplexer

single mode optical fibres

detectors

INSIDE ATLAS

meter

wave-

CLO

CK

DISC

RIM

INAT

ORS

refe

renc

eetalons

retroreflectors

Figure 9-17 Conceptual design of a FSI jewel.

Fibre strain rel iefs Bend radius ~1cm

Retro-ref lectorIn ject /Receive Windows

Carbon f ibre frame bal l

Mount ing Stud


9 Alignment 237

typed. Figure 9-17 shows a conceptual view of such a modular jewel for use in the forward re-gion. It consists of a sphere of about 1 cm diameter, through which the ferrules containing thefibres are mounted via precision holes. The surface of the sphere also provides mounting loca-tions for the retro-reflectors, a mechanical mounting fixture to attach the jewel to the detectorspace frame and some fiducials to allow the position of the jewel to be surveyed relative to thespace-frame. A series of prototype mounting spheres are under construction and these will becombined into a test-grid with the demonstration FSI system before the design is finalised

9.3.4.4 Laboratory Test Results

A laboratory demonstration system has been assembled in order to check the validity of the ba-sic principles introduced above and for the development of a prototype survey system for AT-LAS. The system currently consists of a single remote interferometer illuminated with a tunablesemiconductor diode laser operating at near-infra-red wavelengths. This 20 mW external cavitylaser has a centre wavelength of 830 nm, a tuning range of ±10 nm and a linewidth of less than

. The interference fringes are detected using a photomultiplier. The optical frequency ofthe laser is measured using a system based on a thermally stabilised reference interferometer,together with a pair of etalons and a wavemeter for determining the correct order number of theinterferometer fringes. The scan control and data acquisition are based on a PC with a VME in-terface. A realistic optical power level and data acquisition bandwidth were used.

The interferometer used in the demonstrationsystem is optically similar to the one proposedfor use within ATLAS and is operated within arange of parameters similar to that of the finalsystem. The ends of two standard 100 m-longsingle-mode optical fibres are mounted paral-lel to each other, about 1 mm apart in a metalblock secured to a vibration-damped opticaltable. The two free fibre ends are connected tothe laser and to a photomultiplier. The half an-gle of the Gaussian laser cone emitted fromthe delivery fibre (and conversely the accept-ance angle of the return fibre) is about 5°. Athin glass plate mounted with a variable orien-tation at a distance of ~ 1 cm from the fibremounting block is used as a beamsplitter. Theretro-reflector is a 7mm diameter prism cor-ner-cube placed at a variable range of between10 cm and 1.5 m from the fibres.

Clear FSI fringes have been observed as shown in Figure 9-18. With an estimated input opticalpower of 10 mW, a clear fringe signal is detectable up to a range in excess of 1.2 m. An accepta-ble signal-to-noise ratio is maintained at sampling rates of more than 1 kHz for the shorter rang-es. At present, the precision of the measurements is limited by the accuracy with which the laserfrequency can be measured. The thermally stabilised reference interferometer (see Figure 9-16)is currently being optimised to allow full-precision absolute distance measurements to be made.

The use of single-mode fibres makes the fringe signal intrinsically insensitive to the mechanicalstate of the fibre. Invariance of the interference signal under mechanical deformation of the fi-bres has been demonstrated experimentally. As foreseen, fringes were obtained for any position

1 MHz

Figure 9-18 FSI Interferometry fringes. The fringeswere taken over a period of 2s while the laser wastuned over an optical frequency of 1.72 GHz, startingat a wavelength of 836.00 nm. The fringes were digi-tised at a rate of 100 Hz. the measured optical pathdifference was 323 mm.

0

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238 9 Alignment

of the corner-cube lying within the Gaussian laser cone. The fringe amplitude is dependentupon the fibre-retro-reflector distance and upon the transverse position of the retro-reflector inthe laser cone. No precise angular positioning of the corner-cube is needed in order to obtainfringes.

The received signal is relatively insensitive to light reflected from objects placed in the lasercone (but not obscuring the line of sight to the retro-reflector). Even white objects may be placedin the beam with only a small effect on the received fringe signal. Operation of the interferom-eter through a black plastic tube was demonstrated successfully, indicating that light thin tubesor screens could be used to protect lines of sight or to prevent light leakage between one inter-ferometer and another.

9.3.5 Straightness Monitors

The Straightness Monitors (SM) have been developed for use in optical multi-point alignment(MPA-ALMY) systems. Such a system will be used for the alignment of the ATLAS muon cham-bers. A modified version of this system is being developed for use in the Inner Detector. TheMPA-ALMY uses collimated laser beams and semi-transparent optical position sensors whichmonitor a common laser ray [9-13]. The optical position sensors are custom designed amor-phous silicon strip photodiodes which are semi-transparent in the red to infra-red wavelengthrange. Collimated laser beams with Gaussian beam profiles and high pointing stability are pro-duced by semiconductor laser diodes connected to collimator optics via single-mode optical fi-bres. The sensors are designed to provide two-dimensional position measurement for theincident laser beam with a precision of order 1 μm over large measurement areas of up to 30times 30 mm2. Since the photo-sensitive material is amorphous silicon, the high position resolu-tion of the sensors is expected to be insensitive to very high magnetic fields (due to the low Hallconductivity and the thin layer of amorphous silicon (see Table 9-10) and to high irradiationdoses. With sensor transmittances of better than 90%, more than 10 sensors can be aligned alongone laser beam without loss in position resolution [9-15].

9.3.5.1 Light Distribution System

Laser light at wavelengths of 690 nm and 780 nm for which the sensors are semi-transparent(see Table 9-10) is produced by semiconductor laser diodes (GaAlAs and GaAlP) coupled to sin-gle-mode optical fibres which only transmit the TEM00 mode. Collimator optics connected tothe single-mode fibres produce diffraction limited laser beams with a Gaussian beam profile.The laser beam diameter over a distance of 2 m can be limited to values between 1.9 and 2.1mm. Using commercial fibre splitters, the light of each laser diode can be distributed to severalalignment monitors over long distances [9-16]. The laser diodes can be installed in accessible lo-cations outside the high irradiation zones. Only the collimator optics have to be installed in theInner Detector itself. Miniaturised lens systems optimised for the alignment of the Inner Detec-tor (see for example [9-16]) have to be developed.


9 Alignment 239

9.3.5.2 Amorphous Silicon Strip Sensors

The optical sensors combine high position res-olution over a large sensitive range with highlight-transmission rates. They consist of a thinfilm of hydrogenated amorphous silicon(a-Si:H) deposited between two layers of indi-um-tin oxide (ITO) electrodes on a glass sub-strate (see Figure 9-19). The top electrodesform Schottky diodes with the amorphous sili-con while the bottom electrodes act as ohmiccontacts.

The top and bottom ITO electrodes are seg-mented with photolithographic methods intotwo orthogonal rows of strips forming dou-ble-sided silicon strip photodiodes. The laser light absorbed by the amorphous silicon generatesphoto-currents on the strips. The laser spot position on the sensor is determined as the cen-tre-of-gravity of the signal strip current distribution. This principle allows for high position res-olution and linearity of the position measurement over large sensitive areas. High uniformity ofthe signal response is achieved due to the full sensitivity of the thin a-Si layer; the charge carrierdiffusion length in amorphous silicon (~ 1 μm) is larger than the film thickness. The characteris-tics of the two types of tested sensors are summarized in Table 9-10.

Table 9-10 Characteristics of amorphous silicon strip sensors.

Sensor Type Type I Type II

Transmittance > 80% > 90%

Wavelength (nm) 690 780

Sensitivity (A/W) 0.1 0.01

Bias voltage (V) 1 3

Size (mm2) 25 · 25

Active area (mm2) 20 · 20

Number of strips 2 · 64

Strip pitch (μm) 312

Strip gap (μm) 10

Strip width (μm) 300

Strip thickness (nm) < 100

a-Si thickness (μm) < 1

Glass thickness (mm) 0.5

Hall mobility μHp (cm2/Vs) 10-4

Hall mobility μHn (cm2/Vs) 10-2 - 10-3

Figure 9-19 Amorphous silicon detector.

Laser beam

ITOa-Si:HGold pad

Glass substrate


240 9 Alignment

The existing device parameters have been optimised for the requirements for the alignment sys-tem of the ATLAS muon spectrometer where the MPA-ALMY monitors will be used. For opticalstraightness monitors to be used in the ATLAS Inner Detector, sensors of sizes 5 · 5 mm2 will beused.

The sensors are manufactured by EG&G Heimann Optoelectronics in Germany. The sensor lay-ers are deposited with plasma enhanced CVD techniques as thin films on an ~ 0.5 mm thickglass substrate (this technique is also used for the fabrication of large area solar cells). The hy-drogen concentration of the amorphous silicon, controlled by the process temperature, is essen-tial for the electrical and optical properties of the sensors. The optical absorption coefficient ofamorphous silicon, with an effective band-gap of ~820 nm, drops fast towards the red end of thevisible spectrum and decreases with increasing hydrogen concentration.

The thicknesses of the sensor layers have been optimised for maximum transmittance, i.e. mini-mum absorption and reflection rate for different wavelengths from the visible red to the near in-fra-red range emitted by GaAs laser diodes [9-15]. The a-Si layer thickness varies between 0.5and 1 μm. The ITO films are 50-100 nm thick with about 95% transmittance in the visible wave-length range.

For λ = 690 nm, transmission rates above 80% have been achieved for the corresponding opti-mised sensor version with 0.5 μm a-Si thickness (type I) while the second sensor type with a 1μm thick amorphous silicon layer (type~II) transmits more than 90% of the incident light for a790 nm wavelength. Further improvement of the transmittance is possible with antireflectivecoating of the back-side of the glass substrate. The spectral sensitivities and recommended biasvoltages for the two sensor types are given in Table 9-10. For large distance applications of mul-ti-point monitors with sensors used in transparent mode, uncertainties in the deflection of thelaser beam by the sensors due to thickness variations and surface roughness have to be takeninto account [9-13]. For cost reasons, commercially available polished sheet glass developed forthe large scale production of liquid-crystal displays has been used for the sensor substrates. Thea-Si sensors are expected to be less sensitive to irradiation than crystalline silicon detectors be-cause of the thin active layer and the nature of the amorphous undoped material.

Degradation of the transmittance of the glass substrate due to irradiation can be avoided by theappropriate choice of glass. Amorphous silicon sensors and glass substrates with the standardglass type have been irradiated at the ISIS spallation source at Rutherford Laboratory with dos-es of 1-2 1014 neutrons/cm2. No degradation of the transmission rates of sensors and glass sub-strates has been observed.

9.3.5.3 Integrated Readout Electronics

The lasers are operated in continuous mode and the sensors are read out continuously with theinternal clock frequency of their electronics.The readout electronics of the strip sensors [9-17] isdesigned to require no calibration. The photo-currents on the strips are multiplexed, amplifiedby a common current voltage transformer, digitised by an 11-bit ADC and stored in a localmemory which can be addressed via a custom designed VME interface board [9-17].

The maximum photo-current on an individual strip is 5 μA. The typical noise level from the de-tector and the electronics is ~ 0.1% of the maximum signal on a strip. Very good chan-nel-to-channel stability on the order of ~ 0.1% has been achieved.


9 Alignment 241

For cost and space reasons, an integrated version of the readout electronics, a 64-channel ana-logue-digital CMOS chip [9-18], has been developed and tested. 2000 ASIC chips have been pro-duced for the next series of prototypes with integrated readout electronics. The top and bottomstrip rows are each read out by one ASIC chip. Controller and interface chips transmit the datato a VME interface board which reads data from 16 sensors. For the ATLAS Inner Detector, thesensor readout electronics will be placed outside the active volume (where the radiation level istolerable) in order to minimise the amount of material in the tracker. The sensors have to be con-nected to the readout electronics via 3-5 m long shielded low-mass cables. Such a readoutscheme is currently under investigation. First laboratory tests of the readout of the 64 · 64 stripsof a 20 · 20 mm2 sensor via 5 m long unshielded ribbon cables showed no significant degrada-tion of the signal-to-noise ratio.

9.3.5.4 Test Results

Extensive tests of 150 20 · 20 mm2 sensors equipped with prototype readout electronics [9-18]and precision mounting frames have been performed [9-13], [9-19]. About half of the sensorswere of type I, the other half of type II (see Table 9-10). The VME-based data acquisition systemdesigned for the readout of large numbers of sensors and the analysis software are described in[9-13], [9-18]. A large part of the tested sensors and the DAQ system are now in use at the AT-LAS alignment test stand DATCHA 0 at Saclay and in the HERA-B silicon-vertex and trackingdetectors where long-term stability tests are under way.

Due to the low noise level, the local position resolution of the sensors is a fraction of a micron.The photo-current measurements are averaged over 20 readout cycles. The photo-current distri-butions on the top and bottom strips are fitted with a Gaussian distribution.

For applications which require a large measurement range, the linearity of the position meas-urement over the active area of the sensors is important. For larger distances between consecu-tive sensors positioned along a laser beam, variations in the deflection angle of the traversinglaser beam caused by refraction in the sensor glass substrate also have to be controlled. Theseeffects have been studied by scanning the sensor surfaces with a laser beam of 690 nm wave-length and 2-4 mm diameter in steps of 300 μm using a computer controlled stepping motor.Details of the results are given in reference [9-19].

Over the 20 · 20 mm2 active area of the tested sensors, position resolutions of a few micronshave been achieved [9-19]. The remaining non-linearity is due to thickness variations of theamorphous silicon layer which will be further reduced in the production process. However forthe smaller area sensors planned for the Inner Detector where the expected displacements of thesensors relative to the laser beam are only on the order of 100 μm, the non-linearity is very smalland the position resolution is about 1 μm. Over the same measurement range, uncorrected vari-ations in the beam deflection angle are only 1-2 μrad [9-13] which is acceptable for applicationsin the ATLAS Inner Detector.


242 9 Alignment

9.3.6 Use of Tracks from Collisions

The ultimate precision for the alignment of the Inner Detector will come from the analysis oftracks from collisions. For this to work, it is essential that either the detector is stable over suffi-ciently long periods of time to perform such an alignment, or that the short term distortions ofthe detector can be corrected for by the optical alignment techniques described above. The rateof high pT tracks from collisions which could be used for alignment is very large even at low lu-minosity. The rates for high pT muons [9-7] is given in Table 9-11 below.

The rate at which the low threshold single muon triggers can be recorded by the data acquisi-tion system will depend on details of the trigger/DAQ architecture, but will probably be in therange 100 Hz-1kHz. The track-based alignment procedures for the TRT and SCT/pixels are de-scribed in the following sections.

9.3.6.1 TRT Track Alignment

The track alignment for the TRT straws will beperformed using the tracks reconstructed inthe precision tracker. Such a procedure hasbeen demonstrated successfully with testbeam data from the TRT sector prototype (seeSection 12.2.4). In the test beam set-up a silicontelescope was used to determine the positionsof the wires. The accuracy of the wire align-ment as a function of the number of tracksused is shown in Figure 9-20. It can be seenthat approximately 100 tracks per straw areneeded to achieve the 30 μm alignment re-quirement for the TRT. From the expected rateof muons (see Section 9.3.6) the time requiredto acquire the data for a track-based alignmentof the TRT would be less than 24 hours.

9.3.6.2 SCT/Pixel Track Alignment

The proposed SCT and pixel track alignment procedure is based on the following procedure:

1. Use the module overlaps in the Rφ and z directions to determine the alignment of themodules with respect to one another. For this purpose the low pT muons will be suitable.

Table 9-11 Level 2 muon trigger rates at low luminosity (1033 cm-2s-1).

Trigger Type Rate (Hz)

Single muon with pT > 6 GeV 4000

1.3

5.0

Z μμ→

W μν→

Figure 9-20 Accuracy of the wire alignment as a func-tion of the number of tracks.

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

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nmen

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y (m

m)


9 Alignment 243

Assuming 100 tracks are required to fix the overlap of two neighbouring modules thenthe time required to collect sufficient data would be of the order of 24 hours;

2. Use the sample of high pT muons from W/Z decays to align each layer with respect toeach other and to correct for distortions of the structure. For this purpose, high pT muonsare preferred since the momentum constraint is much more powerful than for low pTmuons which are in the multiple scattering dominated regime. To determine simple pa-rameters like rotations of one barrel with respect to each other the time taken to collectsufficient data will be only of the order of minutes. However to correct for more compli-cated distortions much more data will be required.

Work on this analysis is now in progress.

9.4 References

9-1 TRACKERR version 1.44, written by W. Innes, SLAC. Available by anonymous ftp from<ftp://ftp/SLAC.Stanford.edu/software/trackerr>.

9-2 S. Snow and A. R. Weidberg, “Alignment requirements for the Inner Detector”, ATLASInternal Note INDET-NO-160 (1997).

9-3 R. Jones and C. Wykes, Holographic Speckle Interferometry, Cambridge Studies inModern Optics 6, Cambridge University Press (1983).

9-4 A. Reichold, Ph.D. Thesis, University of Dortmund (1996).

9-5 K. Cerath, “Phase Measurement Interferometry Techniques”, Progress in Optics XXVI ,(1988) 351.

9-6 ATLAS Internal Note in preparation, “X-ray alignment for the SCT”.

9-7 ATLAS Technical proposal, CERN/LHCC/94-43, LHCC/P2 (1994).

9-8 Catalogue: “AEROTECH Motion Control Product Guide” (1993) 77.

9-9 A.F. Fox-Murphy et. al., “Frequency Scanned Interferometry (FSI): The basis of a surveysystem for the ATLAS Inner Detector using fast automated remote interferometry”,ATLAS Internal Note INDET-NO-112 (1996).

9-10 A.F. Fox-Murphy et. al., “Frequency scanned interferometry (FSI): the basis of a surveysystem for ATLAS using fast automated remote interferometry”, Nuclear Instrum.Methods A383 (1996) 229.

9-11 A.F. Fox-Murphy, Development of a novel alignment system for the ATLAS InnerDetector and an investigation of the effect of alignment inaccuracies on trackerperformance, D. Phil. thesis, University of Oxford, 1996.

9-12 SCAN-3, “System for Analysis of Geodetic Networks”, Release 2.1, Geodetic ComputingCentre, Delft University of Technology, The Netherlands (1995).

9-13 W. Blum, H. Kroha and P. Widmann, “A Novel Laser-Alignment System for TrackingDetectors Using Transparent Silicon Strip Sensors”, Nuclear Instrum. Methods A367(1995) 413; ”Transparent Silicon Strip Sensors for the Optical Alignment of ParticleDetector Systems”, Nuclear Instrum. Methods A377 (1996) 404; “A Novel laser alignmentsystem for Particle Tracking Using Transparent Silicon Strip Sensors”, IEEE Trans.Nuclear Science, Vol. 43, No. 3 (1996) 1194.


244 9 Alignment

9-14 H. Kroha, “Laser Alignment System with Transparent Silicon Strip Sensors and itsApplications”, MPI report, MPI-PhE 96-20 (1996).

9-15 V. Bartheld, Diploma Thesis, Technical University, Munich, MPI report,MPI-PhE/97-04, (1997).

9-16 P. Widmann, Diploma Thesis, Ludwig-Maximilians University. Munich (1994), MPIreport, MPI-PhE/94-21 (1994).

9-17 B. Dulny, J. Fent and H. Kroha,”Manual for Transparent Silicon Strip-Sensor Readout”,MPI report, MPI-PhE/96-08, (1996).

9-18 B. Dulny, J. Fent and H. Kroha, ASIC chip for Alignment Strip-Sensor Readout, MPIreport, MPI-PhE/96-14, (1996).

9-19 V. Bartheld, H. Kroha and S. Schael,” Serial Test of Transparent Silicon Strip Sensors forthe Alignment System of the ATLAS Muon Spectrometer”, ATLAS Internal Note inpreparation.


A Members of the ATLAS Collaboration 245

A Members of the ATLAS Collaboration

ArmeniaYerevan Physics Institute, YerevanAirapetian A., Grabsky V., Hakopian H., Vartapetian A.

AustraliaResearch Centre for High Energy Physics, Melbourne University, MelbourneFares F., Moorhead G.F., Sevior M.E., Taylor G.N., Tovey S.N.Australian Nuclear Science and Technology Organisation, SydneyAlexiev D., Donnelly I.J., Varvell K.E., Williams M.L.University of Sydney, SydneyHashemi-Nezhad R., Peak L., Saavedra A., Ulrichs J.

AustriaInstitut für Experimentalphysik der Leopold-Franzens-Universität Innsbruck, InnsbruckGirtler P., Kiener Ch., Kneringer E., Kuhn D., Rudolph G.

Azerbaijan RepublicInstitute of Physics, Azerbaijan Academy of Science, BakuAbdinov O.B., Aliyev F.M., Khalilzade F.T., Mekhdiyev R.R., Rzayev H.J., Usubov Z.U.

Republic of BelarusInstitute of Physics of the Academy of Science of Belarus, MinskBaturitsky M.A., Bogush A.A., Demchenko A.I., Gazizov A.Z., Gilevsky V.V., Golubev V.S., Levchuk M.I.,Satsunkevich I.S., Shevtsov V.V.

BrazilUniversidade Federal do Rio de Janeiro, COPPE/EE/IF, Rio de JaneiroCaloba L.P., Galvez-Durand F., Maidantchik C.L., Marroquim F., Seixas J.M., Thome Z.D.Instituto de Fisica, Universidade de Sao Paulo, Sao PauloDaSilva N.C., Dietzsch O., Leite M.A.L., Sakanoue M.H., Takagui E.M., Zandona F.

CanadaUniversity of Alberta, EdmontonArmstrong W.W., Burris W., Davis R., Gingrich D. M., Hewlett J.C., Holm L., Macpherson A.L., Mullin S.,Pinfold J.L., Schaapman J., Soukup J., Wampler L.Department of Physics, University of British Columbia, VancouverAxen D., Mayer J.K., Orr R.S.University of Carleton/C.R.P.P., CarletonArmitage J., Dixit M., Dubeau J., Estabrooks P., Losty M., Neuheimer E., O’Neil M., Oakham G.Group of Particle Physics, University of Montreal, MontrealAzuelos G., Ben El Fassi A., Depommier P., Leon-Florian E., Leroy C., Martin J.P., Marullo F., Roy P.,Savard P.Department of Physics, University of Toronto, TorontoBailey D.C., Bhadra S., Martin J.F., Sinervo P.K., Stairs G.G., Trischuk W.TRIUMF, VancouverAstbury A., Birney P., Hodges T., Langstaff R., Oram C., Roberts B., Rosvick M., Wellisch H.P.University of Victoria, VictoriaBishop S., Fincke-Keeler M., Honma A., Keeler R., Lefebvre M., O’Neil D., Poffenberger P., Roney M.,Sobie R.

CERNEuropean Laboratory for Particle Physics (CERN), GenevaAnghinolfi F., Bachy G., Barberio E., Benincasa G., Bergsma F., Bjorset L., Blocki J., Bloess D., Bock R.,Bogaerts J., Brawn I., Burckhart H.J., Butin F., Campbell M., Chesi E., Chevalley J.L., Christiansen J.,Cobal M., Dabrowski W., Dauvergne J.P., Dell’Acqua A., Denes E., Dittus F., Dobinson R.,


246 A Members of the ATLAS Collaboration

Drakoulakos D., Dufey J.P., Dydak F., Eerola P., Efthymiopoulos I., Ellis N., Fabjan C.W., Farthouat P.,Flegel W., Francis D., Froidevaux D., Gebart R., Gianotti F., Gildemeister O., Hatch M., Haug F.,Hauviller C., Heeley R., Heijne E., Henriques A., Hervas L., Hoffmann H.F., Hortnagl C., Jarp S., Jarron P.,Jenni P., Jones R., Kantardjian G., Kaplon J., Kliouchnikova T., Knobloch J., Koski K., Kotz U., Lacasta C.,Langhans W., Lasseur C., Lehraus I., Lemeilleur F., Lichard P., Liebhart M., Linde F., Lofstedt B.,Madsen N., Mapelli L., Marchioro A., Martin B., Mauguin J.-M., McLaren R.A., Meier D., Michelotto M.,Mornacchi G., Myers D., Nessi M., Nicquevert B., Onions C., Pailler P., Patel A., Poggioli L., Poppleton A.,Posch C., Poulard G., Price M., Riedler P., Riegler W., Roe S., Rohrbach F., Rousseau D., Rudge A.,Ryjov V., Schaller M., Schmid P., Schmitt M., Schuler G., Snoeys W., Soloviev I., Spegel M., Spiwoks R.,Stavrianakou M., Stavropoulos G., Tartarelli G.F., Taylor B., Ten Kate H., Treichel M., Van der Bij H.,Vasey F., von Boehn-Bucholz R., Voss R., Vreeswijk M., Vuillemin V., Weilhammer P., Wendler H.,Werner P., Witzeling W., Wotschack J.

Czech RepublicAcademy of Sciences of the Czech Republic, Institute of Physics, PragueBoehm J., Hrivnac J., Lednicky R., Lokajicek jr M., Nemecek S., Sicho P., Simak V., Stastny J., Stedron M.,Vanickova M., Vrba V.Charles University, Faculty of Mathematics and Physics, PragueDavidek T., Dolejsi J., Dolezal Z., Kucera M., Leitner R., Soustruznik K., Suk M., Tas P., Trka Z., Valkar S.,Wilhelm I., Zdrazil M.Czech Technical University in Prague, Faculty of Nuclear Sciences and Physical Engineering, Faculty ofMechanical Engineering, PragueJakubek J., Kubasta J., Macha I., Ota J., Pospisil S., Sinor M., Sopko B., Tomiak Z.

DenmarkNiels Bohr Institute, University of Copenhagen, CopenhagenDam M., Hansen J.D., Hansen J.R., Hansen P., Rensch B.

FinlandHelsinki Institute of Physics, HelsinkiJalas P., Schulman T.

FranceLaboratoire d’Annecy-le-Vieux de Physique des Particules (LAPP), IN2P3-CNRS, Annecy-le-VieuxAubert B., Colas J., Eynard G., Jezequel S., Linossier O., Massol N., Minard M.N., Nicoleau S., Perrodo P.,Sauvage G., Wingerter-Seez I., Zitoun R., Zolnierowski Y.Université Blaise Pascal, IN2P3-CNRS, Clermont-FerrandBrette Ph., Chadelas R., Chevaleyre J.C., Crouau M., Daudon F., Grenier P., Hebrard C., Montarou G.,Pallin D., Poirot S., Reinmuth G., Santoni C., Says L.P., Vazeille F.Institut des Sciences Nucléaires de Grenoble, IN2P3-CNRS-Université Joseph Fourier, GrenobleAndrieux M.L., Ballon J., Collot J., Dzahini D., Ferrari A., Guerre-Chaley B., Hostachy J.Y., Laborie G.,Martin Ph., Pouxe J., Rabier C., Rey-Campagnolle M., Rossetto O., De Saintignon P., Stassi P., Wielers M.Centre de Physique des Particules de Marseille, IN2P3-CNRS, MarseilleBasa S., Blanquart L., Bonzom V., Calzas A., Checkhtman A., Clemens J-C., Cohen-Solal M.,Cousinou M-C., Dargent P., Delpierre P., Dinkespiler B., Duval P-Y., Etienne F., Fallou A., Fassnacht P.,Ferrato D., Fouchez D., Gally Y., Grigoriev E., Habrard M-C., Hallewell G., Le Van Suu A., Martin L.,Mekkaoui A., Monnier E., Mouthuy T., Nacasch R., Nagy E., Nicod D., Olivetto C., Pouit L., Quian Z.,Raymond M., Rondot C., Rozanov A., Sauvage D., Tisserant S., Touchard F., Vacavant L.Laboratoire de l’Accélérateur Linéaire, IN2P3-CNRS, OrsayArdelean J., Arnault C., Auge E., Barrand G., Belot G., Bouchel M., Boucrot J., Breton D., Chollet C.,Coulon J-P., De la Taille C., Delebecque P., Ducorps A., Fayard L., Fournier D., Gonzales J., Grivaz J-F.,Hrisoho A., Iconomidou-Fayard L., Imbert P., Jacquier Y., Jean Ph., Lavigne B., Mace G.,Martin-Chassard G., Merkel B., Nikolic I., Noppe J-M., Parrour G., Petroff P., Puzo P., Richer J-P.,Schaffer A-C., Seguin-Moreau N., Serin L., Tisserand V., Togut V., Unal G., Vales F., Veillet J-J., Vernay E.LPNHE, Universités de Paris VI et VII, IN2P3-CNRS, ParisAlexanian H., Baubillier M., Bezamat J., Billoir P., Blouzon F., Canton B., David J., Genat J-F., Imbault D.,Le Dortz O., Nayman P., Rossel F., Savoy-Navarro A., Schwemling P.



CEA, DSM/DAPNIA, Centre d’Etudes de Saclay, Gif-sur-YvetteBelorgey J., Bernard R., Berriaud C., Berthier R., Borgeaud P., Bourdinaud M., Bystricky J., Calvet D.,Chalifour M., Chevalier L., Cloué O., Daël A., Delagnes E., Desages F., Desportes H., Ernwein J.,Gachelin O., Gallet B., Giacometti J., de Girolamo P., Gosset L., Guyot C., Hansl-Kozanecka T.,Heitzmann J., Hubbard J.R., Huet M., Kozanecki W., Laporte J.F., Le Dû P., Lesmond C., Lottin J-P.,Lugiez F., Mandjavidze I., Mansoulié B., Mayri C., Molinié F., Mur M., Pabot Y., Pascual J., Pelle J.,Perrin P., Pinabiau M., Renardy J.F., Schuller J.P., Schune Ph., Schwindling J., Simion S., Smizanská M.,Taguet J.P., Teiger J., Thooris B., Tirler R., Van Hille H., Veenhof R., Veyssiere C., Virchaux M., Walter C.

Republic of GeorgiaInstitute of Physics of the Georgian Academy of Sciences, TbilisiChikovani L., Gabunia L., Gogiberidze G., Gogoladze G., Grigalashvili T., Khorguashvili Z., Kipiani K.,Koshtoev V., Sopromadze D., Topchishvili L., Tvalashvili O.Tbilisi State University, TbilisiChiladze B., Djobava T., Khelashvili A., Khubua J., Liparteliani A., Metreveli Z., Mosidze M.,Salukvadze R.

GermanyPhysikalisches Institut, Universität Bonn, BonnDesch K., Fischer P., Geich-Gimbel C., Hilger E., Meuser S., Ockenfels W., Raith B., Wermes N.Institut für Physik, Universität Dortmund, DortmundBecker C., Fuss J., Goessling C., Lisowski B., Luthaus P., Wunstorf R.Fakultät für Physik, Albert-Ludwigs-Universität, FreiburgBaer Th., Chen J., Ebling D.G., Goeppert R., Herten G., Irsigler R., Kollefrath M., Kolpin R., Landgraf U.,Lauxtermann S., Ludwig J., Mohr W., Paschhoff V., Rehmann V., Rolker B., Runge K., Schaefer F.,Scherberger G., Schmid T., Webel M., Weber C.Institut für Hochenergiephysik der Universität Heidelberg, HeidelbergGeweniger C., Hanke P., Kluge E.-E., Mass A., Putzer A., Tittel K., Wunsch M.Institut für Informatik, Friedrich-Schiller-Universität Jena, JenaDoersing V., Erhard W., Kammel P., Reinsch A.Institut für Physik, Johannes-Gutenberg Universität Mainz, MainzBuchholz P., Hoelldorfer F., Jakobs K., Kleinknecht K., Koepke L., Marschalkowski E., Merle K.,Othegraven R., Renk B., Schaefer U., Schue Y., Walkowiak W.Lehrstuhl für Informatik V, Universität Mannheim, MannheimHoegl H., Kugel A., Ludvig J., Manner R., Noffz K-H., Ruhl S., Zoz R.Sektion Physik, Ludwig-Maximilian-Universität München, MünchenDeile M., Dubbert J., Faessler M.A., Hessey N.P., Sammer T., Staude A., Trefzger T.Max-Planck-Institut für Physik, MünchenAckermann K., Aderholz M., Andricek L., Blum W., Bratzler U., Brettel H., Dietl H., Dulny B., Fent J.,Gruhn C., Hauff D., Koffeman E., Kroha H., Lutz G., Manz A., Moser H.-G., Oberlack H., Ostapchuk A.,Richter R., Richter R.H., Schacht P., Schael S., Soergel V., Stenzel H., Striegel D., Tribanek W.Fachbereich Physik, Universität Siegen, SiegenGillessen G., Holder M., Kreutz A.Fachbereich Physik, Bergische Universität, WuppertalBecks K.H., Braun H., Drees J., Gerlach P, Glitza K.W., Hamacher K., Kersten S., Lenzen G., Linder C.,Thadome J., Wahlen H.

GreeceAthens National Technical University, AthensDris M., Filippas A., Fokitis E., Gazis E., Katsoufis E., Maltezos S., Papadopoulou T.Athens University, AthensGiokaris N., Ioannou P., Kourkoumelis C., Papadopoulos I., Tatsis S., Tzanakos G.S.Aristotle University of Thessaloniki, ThessalonikiBouzakis C., Chardalas M., Chouridou S., Dedoussis S., Gavris G., Lagouri Th., Liolios A., Paschalias P.,Petridou C., Sampsonidis D., Sergiadis G., Zamani M.



IsraelDepartment of Physics, Technion, HaifaDado S., Goldberg J., Lupu N.Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics and Astronomy, Tel-Aviv University,Tel-AvivAbramowicz H., Alexander G., Bella G., Benary O., Dagan S., Grunhaus J., Oren Y.Department of Particle Physics, The Weizmann Institute of Science, RehovotBreskin A., Chechik R., Duchovni E., Eisenberg Y., Gross E., Hass M., Karshon U., Lellouch D.,Levinson L., Mikenberg G., Revel D.

ItalyDipartimento di Fisica dell’ Università della Calabria e I.N.F.N., CosenzaArneodo M., Ayad R., Capua M., La Rotonda L., Schioppa M., Susinno G., Valdata-Nappi M.Laboratori Nazionali di Frascati dell’ I.N.F.N., FrascatiBilokon H., Chiarella V., Curatolo M., Esposito B., Ferrer M., Maccarrone G., Pace E., Pepe-Altarelli M.,Spitalieri M., Zuffranieri F.Dipartimento di Fisica dell’ Università di Genova e I.N.F.N., GenovaBarberis D., Bozzo M., Caso C., Dameri M., Darbo G., Gagliardi G., Gemme C., Morettini P., Musico P.,Olcese M., Osculati B., Parodi F., Pozzo A., Ridolfi G., Rossi L., Sette G.Dipartimento di Fisica dell’ Università di Lecce e I.N.F.N., LecceCreti P., Gorini E., Grancagnolo F., Palamara O., Panareo M., Perrino R., Petrera S., Primavera M.Dipartimento di Fisica dell’ Università di Milano e I.N.F.N., MilanoBattistoni G., Bellini G., Bonivento W., Camin D., Cavalli D., Costa G., D’Angelo P., di Corato M.Fedjakin N.N., Ferrari A., Gozzi L., La Banca N., Mandelli L., Mazzanti M., Menasce D., Milazzo L.,Moroni L., Pedrini D., Perasso L., Perini L., Resconi S., Sala P., Sala S.,Dipartimento di Scienze Fisiche, Università di Napoli ‘Federico II’ e I.N.F.N., NapoliAloisio A., Alviggi M.G., Cevenini F., Chiefari G., De Asmundis R., Merola L., Napolitano M., Patricelli S.Dipartimento di Fisica Nucleare e Teorica dell’ Università di Pavia e I.N.F.N., PaviaCambiaghi M., Caselotti G., Conta C., Ferrari R., Fraternali M., Lanza A., Livan M., Polesello G.,Rimoldi A., Vercesi V.Dipartimento di Fisica dell’ Università di Pisa e I.N.F.N., PisaAutiero D., Bellettini G., Bosi F., Cavasinni V., Cologna S., Costanzo D., De Santo A., Del Prete T.,Di Girolamo B., Flaminio V., Lami S., Latino G., Mazzoni E., Paoletti R., Raffaelli F., Renzoni G., Rizzi D.Dipartimento di Fisica dell’ Università di Roma ‘La Sapienza’ e I.N.F.N., RomaBagnaia P., Bini C., Caloi R., Cavallari A., Ciapetti G., De Zorzi G., Falciano S., Gauzzi P., Gentile S.,Lacava F., Luci C., Luminari L., Mirabelli G., Nisati A., Oberson P., Petrolo E., Pontecorvo L.,Veneziano S., Zanello L.Dipartimento di Fisica dell’ Università di Roma ‘Tor Vergata’ e I.N.F.N., RomaCamarri P., Cardarelli R., Di Ciaccio A., Santonico R.Dipartimento di Fisica dell’ Università di Roma ‘Roma Tre’ e I.N.F.N., RomaBacci C., Ceradini F., Orestano D., Pastore F.Dipartimento di Fisica dell’ Università di Udine, Gruppo collegato di Udine I.N.F.N. Trieste, UdineCauz D., D’Auria S., De Angelis A., Pauletta G., Santi L., Scuri B., Waldner F., del Papa C.

JapanDepartment of Information Science, Fukui University, FukuiKawaguti M., Tanaka S.Hiroshima Institute of Technology, HiroshimaAsai M.Department of Physics, Hiroshima University, Higashi-HiroshimaIwata Y., Ohsugi T.KEK, National Laboratory for High Energy Physics, TsukubaAmako K., Arai Y., Fujii H., Ikeno M., Iwasaki H., Kanzaki J., Kohriki T., Kondo T., Manabe A., Morita Y.,Nomachi M., Ohska T.K., Sasaki O., Sasaki T., Terada S., Unno Y., Watase Y., Yamamoto A., Yasu Y.Department of Physics, Faculty of Science, Kobe University, KobeKawagoe K., Nozaki M., Takeda H.



Kyoto University of Education, Kyoto-shiTakashima R.Naruto University of Education, Naruto-shiNagamatsu M., Yoshida H.Department of Physics, Faculty of Science, Shinshu University, MatsumotoTakeshita T.International Centre for Elementary Particle Physics, University of Tokyo, TokyoHasegawa Y., Imori M., Kawamoto T., Kobayashi T., Mashimo T.Physics Department, Tokyo Metropolitan University, TokyoFukunaga C., Hamatsu C.Tokyo University of Agriculture and Technology, Department of Applied Physics, TokyoEmura T.

KazakhstanHigh-Energy Physics Institute of the Kazakh Academy of Sciences, AlmatyBoos E., Pokrovsky N., Zhautykov B.

MoroccoFaculté des Sciences Aïn Chock, Université Hassan II, Casablanca, and Université Mohamed V, RabatChakir H., Cherkaoui R., Hoummada A., Saidi H., Sayouty E.

NetherlandsFOM - Institute SAF NIKHEF and University of Amsterdam/NIKHEF, AmsterdamBakker F.E., Bobbink G.J., Bos K., Boterenbrood H., Buis E.J., Dankers R.J., Daum C., Ferrer M.L.,Groenstege H., Hartjes F., Hendriks P., Heubers W., Kaan B., Kieft G.N.M., Kluit R., Massaro G.G.G.,Meddeler G., Metselaar J., Pace E., Reichold A., Rewiersma P.A.M., Schuijlenburg H., Spelt J.,Spitalieri M., Vermeulen J.C., Werneke P., Woudstra M., Zuffranieri F., van Eijk B., van der Graaf H.University of Nijmegen/NIKHEF, NijmegenBergman R., Brouwer C., Crijns F.J.G.H., Dijkema J.A., Kittel W., Klok P.F., Koenig A.C., Metzger W.J.,Pols C.L.A., Schotanus D.J., Visser E.J., Wijnen Th.A.M.

NorwayUniversity of Bergen, BergenEigen G., Frodesen A.G., Klovning A., Stugu B.University of Oslo, OsloBugge L., Buran T., Kristiansen H., Read A.L., Stapnes S.

PolandHenryk Niewodniczanski Institute of Nuclear Physics, CracowGadomski S., Godlewski J., Hajduk Z., Kisielewski B., Korcyl K., Malecki P., Moszczynski A.,Olszowska J., Richter-Was E., Sobala A.Faculty of Physics and Nuclear Techniques of the Academy of Mining and Metallurgy, CracowGrybos P., Idzik M., Jagielski S., Jelen K., Kiesilewska D., Kowalski T., Rulikowska-Zarebska E.

PortugalLaboratorio de Instrumentação e Física Experimental de Partículas (University of Lisboa, University of Coimbra,University Católica-Figueira da Foz and University Nova de Lisboa), LisbonAmaral P., Amorim A., Carvalho J., Casarejos E., David M., Gomes A., Gomes J., Ivanyuchenkov I.,Maio A., Maneira M., Martins J.P., Onofre A., Pinhao J., Santos J., Silva J., Varanda M., Wolters H.

RomaniaInstitute of Atomic Physics, BucharestArsenescu R., Boldea V., Caprini I., Caprini M., Constantin F., Constantinescu S., Dita P., Dita S.,Legrand I.C., Maniu G., Micu L., Niculescu M., Pantea D., Popeneciu G., Serban T.



RussiaInstitute for Theoretical and Experimental Physics (ITEP), MoscowArtamonov A., Epchtein V., Gorbunov P., Gurin R., Jemanov V., Khovansky V., Koutchenkov A.,Kruchinin S., Maslennikov A., Ryabinin M., Shatalov P., Tsoukerman I., Zaitsev V., Zeldovich S.P.N. Lebedev Institute of Physics, MoscowAkimov A., Baranov S., Belov M., Blagov M., Fedorchuk S., Gavrilenko I., Komar A., Konovalov S.,Kopytine M., Mouraviev S., Popov L., Shikanyan A., Shmeleva A., Snesarev A., Speransky M., Sulin V.,Tikhomirov V., Vassilieva L., Yakimenko M.Moscow Engineering and Physics Institute (MEPhI), MoscowBondarenko V., Dolgoshein B., Konstantinov A., Nevski P., Romaniouk A., Semenov S., Smirnov S.,Sosnovtzev V.Moscow State University, Institute of Nuclear Physics, MoscowBashindjagian G.L., Basiladze S.G., Chudakov E.A., Erasov A.B., Grishkevich Y., Karmanov D.E.,Kramarenko V.A., Larichev A.N., Melikhov D.I., Merkin M.M., Nikitin N.V., Rizatdinova F.K.,Selikov A.V., Sivoklokov S.Yu., Smirnova L.N., Zhukov V.Yu., Zverev E.G.Budker Institute of Nuclear Physics (BINP), NovosibirskBatrakov A., Chilingarov A., Fedotov M., Gaponenko I., Klimenko S., Kollegov M., Kozlov V., Kuper E.,Merzlyakov Y., Panin V., Shamov A., Telnov V., Tikhonov Y., Velikzhanin Y.Institute for High Energy Physics (IHEP), ProtvinoAmelin D.V., Ammosov V.V., Antipov Yu.M., Batarin V., Bogoliubsky M.Yu., Borissov A.A., Borissov E.,Bozko N.I., Bryzgalov V.V., Chekulaev S.V., Denisov S.P., Dushkin A.Yu., Fakhroutdinov R., Fenyuk A.B.,Gapienko V.A., Gilitsky Yu.V., Goryatchev V., Gouz Yu.P., Karyukhin A.N., Khokhlov Yu.A.,Kirsanov M.M., Kiryunin A.E., Klyukhin V., Kojine A., Kononov A.I., Konstantinov V., Kopikov S.V.,Korotkov V.A., Kostrikov M.E., Kostyukhin V.V., Kravtsov V.I., Kulemzin A., Kurchaninov L.L.,Lapin V.V., Levitsky M.L., Los S., Maximov V., Miagkov A.G., Mikhailin V.N., Minaenko A.A.,Moiseev A.M., Onuchin V.A., Pleskach A.V., Salomatin Yu.I., Senko V.A., Shein I., Soldatov A.P.,Solodkov A.A., Solovianov O.V., Starchenko E.A., Sviridov Yu., Sytnik V.V., Tchmil V., Tchountonov A.,Tikhonov V.V., Tsyupa Yu., Usenko E., Vorobiev A.P., Vovenko A.S., Zaets V.G., Zaitsev A.M., Zimin S.,Zmushko V.Petersburg Nuclear Physics Institute (PNPI), Gatchina, St. PetersburgFedin O., Filimonov V., Gavrilov G., Ivochkin V., Khomoutnikov V., Kolos S., Krivchitch A., Lochak I.,Maleev V., Nadtochy A., Patritchev S., Prokofiev D., Riabov J., Schegelsky V., Soloviev I., Spiridenkov E.,Zalite A.

JINRJoint Institute for Nuclear Research, DubnaAlexandrov I., Alexeev G., Alikov B., Anosov V., Astvatsaturov A., Azhgirei L., Bannikov A., Baranov S.,Boyko I., Budagov J., Chelkov G., Cheplakov A., Chirikov-Zorin I., Chlachidze G., Dodonov V.,Feshenko A., Flyagin V., Glagolev V., Golikov V., Golubykh S., Gornushkin Y., Iamburenko V.,Ignatenko M., Juravlev N., Kakurin S., Kalinichenko V., Kazarinov M., Kazymov A., Kekelidze V.,Khasanov A., Khomenko B., Khovansky N., Kotov V., Kovtun V., Krumstein Z., Kukhtin V., Kulchitsky Y.,Kuznetsov O., Ladygin E., Lazarev A., Lebedev A., Ljablin M., Lomakin Y., Malyshev V., Malyukov S.,Merekov Y., Merzljakov S., Minashvili I., Nikolenko M., Nozdrin A., Obudovskij V., Olshevski A.,Peshekhonov V., Pisarev I., Podkladkin S., Pose R., Pukhov O., Romanov V., Rumyantsev V.,Russakovich N., Ryabchenko K., Salihagic D., Samoilov V., Savin I., Scheltckov A., Sedykh Y.,Semenov A., Senchishin V., Shabalin D., Shalyugin A., Shigaev V., Shilov Y., Sissakian A., Snyatkov V.,Sorokina J., Tkachev L., Tokmenin V., Topilin N., Tskhadadze E., Usov Y., Vertogradov L., Vinogradov V.,Vorozhtsov S., Yarygin G., Yatsunenko Y., Zhuravlev V.

Slovak RepublicBratislava University, Bratislava, and Institute of Experimental Physics of the Slovak Academy of Sciences, KosiceBan J., Bruncko D., Chochula P., Dubnickova A., Ferencei J., Jusko A., Kladiva E., Kubinec P., Kurca T.,Masarik J., Povinec P., Rosinsky P., Stanicek J., Stavina P., Strizenec P., Sykora I., Tokar S., Vanko J.



SloveniaJozef Stefan Institute and Department of Physics, University of Ljubljana, LjubljanaCindro V., Filipcic A., Kramberger G., Mikuz M., Tadel M., Zontar D.

SpainInstitut de Física d’Altes Energies (IFAE), Universidad Autónoma de Barcelona, Bellaterra, BarcelonaBlanchot G., Bosman M., Casado P., Cavalli-Sforza M., Chmeissani M., Crespo J.M., Delfino M.,Fernandez E., Grauges E., Ivanyushenkov Y., Juste A., Martinez M., Miralles Ll., Pacheco A., Park I.C.,Perlas J.A., Riu I., Vichou I.Physics Department, Universidad Autónoma de Madrid, MadridBarreiro F., Del Peso J., Hervas L., Labarga L.Instituto de Física Corpuscular (IFIC), Centro Mixto Universidad de Valencia - CSIC, Burjassot, ValenciaAlbiol F., Ballester F., Benlloch J.M., Bernabeu J., Cases R., Castillo M.V., Ferrer A., Fuster J., Garcia C.,Gonzalez V., Gil I., Lopez J.M., Romance J.B., Salt J., Sanchez J., Sanchis E., Sanchis M.A., Sebastia A.,Zuniga J.

SwedenFysika institutionen, Lunds universitet, LundAkesson T., Almehed S., Carling H., Danielson H., Egede U., Hedberg V., Jarlskog G., Korsmo H.,Lorstad B., Lundberg B., Mjornmark U., Soderberg M.Royal Institute of Technology (KTH), StockholmAkerman D., Carlson P., Clement C., Leven S., Lund-Jensen B., Pearce M., Soderqvist J., Vanyashin A.University of Stockholm, StockholmAgnvall S., Berglund S., Bohm C., Engstrom M., Fristedt A., Hellman S., Holmgren S-O., Johansson E.,Jon-And K., Sellden B., Silverstein S., Tardell S., Yamdagni N., Zhao X.Uppsala University, Department of Radiation Sciences, UppsalaBingefors N., Botner O., Brenner R., Bystrom O., Ekelof T., Gustafsson L., Hallgren A., Kullander S.,Staaf P.

SwitzerlandLaboratory for High Energy Physics, University of Bern, BernBeringer J., Borer K., Hess M., Lehmann G., Mommsen R., Pretzl K.Section de Physique, Université de Genève, GenevaBonino R., Clark A.G., Couyoumtzelis C., Demierre Ph., Kambara H., Kowalewski R., La Marra D.,Leger A., Perrin E., Vuandel B., Wu X.

TurkeyDepartment of Physics, Bogaziçi University, IstanbulArik E., Birol I., Cicek Z., Cuhadar T., Gun S., Hacinliyan A., Mailov A., Nurdan K., Perdahci Z., Turk I.,Unel G.

United KingdomSchool of Physics and Space Research, The University of Birmingham, BirminghamCharlton D.G., Dowell J.D., Garvey J., Hillier S.J., Homer R.J., Jovanovic P., Kenyon I.R., McMahon T.J.,O’Neale S.W., Rees D.L., Staley R.J., Watkins P.M., Watson A.T., Watson N.K., Wilson J.A.Cavendish Laboratory, Cambridge University, CambridgeBatley J.R., Carter J.R., Drage L., Goodrick M.J., Hill J.C., Munday D.J., Parker M.A., Robinson D.,Wyllie K.H.Department of Physics and Astronomy, University of Edinburgh, EdinburghBoyle O., Candlin D.J., Candlin E.R.S., Knowles I.G.Department of Physics and Astronomy, University of Glasgow, GlasgowDoyle A.T., Flavell A.J., Lynch J.G., Martin D.J., O’Shea V., Raine C., Saxon D.H., Skillicorn I.O.,Smith K.M.School of Physics and Chemistry, Lancaster University, LancasterBrodbeck T.J., Henderson R.C.W., Hughes G.H., Komorowski T., Ratoff P.N., Sloan T.



Department of Physics, Oliver Lodge Laboratory, University of Liverpool, LiverpoolAllport P.P., Booth P.S.L., Carroll L.J., Cooke P.A., Greenall A., Houlden M.A., Jackson J.N., Jones T.J.,King B.T., Marti-i-Garcia S., Maxfield S.J., Moreton A., Richardson J.D., Smith N.A., Sutcliffe P.,Turner P.R.Department of Physics, Queen Mary and Westfield College, University of London, LondonBeck G.A., Carter A.A., Eisenhandler E.F., Hughes D.M., Kyberd P., Landon M., Lloyd S.L.,Newman-Coburn D., Pentney J.M., Pritchard T.W., Thompson G.Department of Physics, Royal Holloway and Bedford New College, University of London, EghamBlair G.A., George S., Green B.J., Medcalf T., Strong J.A.Department of Physics and Astronomy, University College London, LondonBignall P., Clarke P., Cranfield R., Crone G., Esten M., Jones T., Lane J., Sherwood P.Department of Physics and Astronomy, University of Manchester, ManchesterDuerdoth I.P., Dunne P.W., Finnegan P.F., Foster J.M., Freestone J., Gilbert S.D., Hughes-Jones R.E.,Ibbotson M., Kolya S.D., Loebinger F.K., Marshall R., Mercer D., Snow S., Thompson R.J.Department of Physics, Oxford University, OxfordBibby J.H., Buira-Clarke D., Fox-Murphy A., Grewal A., Harris F.J., Hawes B.M., Hill J., Holmes A.,Howell D., Hunt S.J., Kundu N., Lloyd J., Loken J.G., Nickerson R.B., Renton P.B., Segar A.M.,Wastie R.L., Weidberg A.R.Rutherford Appleton Laboratory, Chilton, DidcotApsimon R.J., Baines J.T., Baynham D.E., Botterill D.R., Campbell D.A., Clifft R.W., Edwards J.P.,Edwards M., English R.L., Fisher S.M., Gee C.N.P., Gibson M.D., Gillman A.R., Hart J.C., Hatley R.W.,Haywood S.J., Hill D.L., Madani S., McCubbin N.A., McPhail D.J., Middleton R.P., Morrissey M.C.,Murray W.J., Nichols A., Norton P.R., Payne B.T., Perera V.J.O., Phillips P.W., Pilling A., Quinton S.P.H.,Saunders B.J., Seller P., Shah T.P., Tappern G.J., Tyndel M., White D.J., Wickens F.J.Department of Physics, University of Sheffield, SheffieldBooth C.N., Buttar C.M., Cartwright S.L., Combley F.H., Lehto M.H., Sellin P.J., Spooner N.J.C.,Thompson L.F.

United States of AmericaState University of New York at Albany, New YorkAlam S., Athar B., Mahmood A., Ovunc S., Severini H., Timm S., Wappler F., Zhichao L.Argonne National Laboratory, Argonne, IllinoisBerger E.L., Blair R., Dawson J., Guarino V., Hill N., May E.N., Nodulman L.J., Price L.E., Proudfoot J.,Schlereth J.L., Stanek R., Wagner R.G., Wicklund A.B.University of Arizona, Tucson, ArizonaCheu E., Johns K., Loch P., Rutherfoord J., Savine A., Shaver L., Shupe M., Steinberg J., Tompkins D.Department of Physics, The University of Texas at Arlington, Arlington, TexasDe K., Gallas E., Li J., Sawyer L., Stephens R., White A.Lawrence Berkeley Laboratory and University of California, Berkeley, CaliforniaBarnett M., Bintinger D., Ciocio A., Dahl O., Einsweiler K., Ely R., Gilchriese M., Haber C., Hinchliffe I.,Holland S., Joshi A., Kipnis I., Kleinfelder S., Milgrome O., Nygren D., Palaio N., Pengg F., Shapiro M.,Siegrist J., Spieler H., Trilling G.Department of Physics, Boston University, Boston, MassachusettsHazen E., Shank J., Simmons E., Whitaker J.S., Zhou B.Brandeis University, Department of Physics, Waltham, MassachusettsBehrends S., Bensinger J.R., Blocker C., Cunningham J., Kirsh L.E., Lamoureux J., Wellenstein H.Brookhaven National Laboratory (BNL), Upton, New YorkCitterio M., Gibbard B., Gordeev A., Gordon H., Graf N., Gratchev V., Kandasamy A., Kotcher J.,Lissauer D., Ma H., Makowiecki D., Murtagh M.J., O’Connor P., Paige F., Polychronakos V.,Protopopescu S., Radeka V., Rahm D.C., Rajagopalan S., Rescia S., Smith G., Sondericker J., Stephani D.,Stumer I., Takai H., Tcherniatine V., Yu B.University of Chicago, Enrico Fermi Institute, Chicago, IllinoisAnderson K., Blucher E., Evans H., Glenzinsky D., Merritt F., Oreglia M., Pilcher J., Pod E., Sanders H.,Shochet M., Turcot A.



Nevis Laboratory, Columbia University, Irvington, New YorkCartiglia N., Cunitz H., Dodd J., Gara J., Leltchouk M., Parsons J., Seman M., Shaevitz M., Sippach W.,Willis W.Department of Physics, Duke University, Durham, North CarolinaFortney L.R., Goshaw A.T., Lee A.M., Oh S.H., Robertson R.J., Wang C.H., Wesson D.Department of Physics, Hampton University, VirginiaBaker K.Department of Physics, Harvard University, Cambridge, MassachusettsFeldman G.J., Franklin M.E.B., Huth J., Oliver J.Indiana University, Bloomington, IndianaHanson G., Luehring F., Ogren H., Rust D.R.University of California, Irvine, CaliforniaFahlund T., Hackett C., Lankford A.J., Pier S., Schernau M., Stoker D.Massachusetts Institute of Technology, Department of Physics, Cambridge, MassachusettsHaridas P., Osborne L.S., Paradiso J.A., Pless I.A., Taylor F.E., Wadsworth B.F.Michigan State University, Department of Physics and Astronomy, East Lansing, MichiganAbolins M., Brock R., Bromberg C., Edmunds D., Ermoline Y., Gross S., Huston J., Laurens P.,Linnemann J., Miller R., Owen D., Pope B.G., Richards R., Weerts H.University of New Mexico, New Mexico Center for Particle Physics, AlbuquerqueGold M., Gorfine G., Matthews J., Seidel S.Physics Department, Norfolk State University, VirginiaKhandaker M., McFarlane K., Punjabi V., Salgado C.W.Physics Department, Northern Illinois University, DeKalb, IllinoisFortner M., Sirotenko V.I., Willis S.E.Department of Physics and Astronomy, University of OklahomaGutierrez P., McMahon T., Nemati B., Skubic P., Snow J., Strauss M.Department of Physics, University of Pennsylvania, Philadelphia, PennsylvaniaDressnandt N., Keener P., Newcomer F.M., Van Berg R., Williams H.H.University of Pittsburgh, Pittsburgh, PennsylvaniaCleland W.E., Clemen M.Department of Physics and Astronomy, University of Rochester, Rochester, New YorkBazizi K., England D., Ferbel T., Ginther G., Glebov V., Haelen T., Lobkowicz F., Slattery P., Zielinski M.Institute for Particle Physics, University of California, Santa Cruz, CaliforniaDorfan D., Dubbs T., Grillo A., Heusch C., Kashigin S., Litke A., Popelvine P., Sadrozinski H., Seiden A.,Spencer E.Department of Physics, Southern Methodist University, Dallas, TexasCoan T.E., Olness F., Stroynowski R., Teplitz V.Tufts University, Medford, MassachusettsMann A., Milburn R., Napier A., Sliwa K.High Energy Physics, University of Illinois, Urbana, IllinoisDowning R.W., Errede D., Errede S., Haney M.J., Simaitis V.J., Thaler J.Department of Physics, Department of Mechanical Engineering, University of Washington, Seattle, WashingtonBurnett T.H., Chaloupka V., Cook V., Daly C., Davisson R., Forbush D., Guldenmann H., Lubatti H.J.,Mockett P.M., Reinhall P., Rothberg J., Wasserbaech S., Zhao T.Department of Physics, University of Wisconsin, Madison, WisconsinFasching D., Gonzalez S., Jared R.C., Pan Y.B., Scott I.J., Walsh J., Wu S.L., Yamartino J.M., Zobernig G.


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